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diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..267df00 --- /dev/null +++ b/.gitignore @@ -0,0 +1,4 @@ +.DS_Store +.idea +*.log +tmp/ diff --git a/articles/discord.html b/articles/discord.html deleted file mode 100755 index 5e657c7..0000000 --- a/articles/discord.html +++ /dev/null @@ -1,215 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2024-03-01 Fri 15:06 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>**Discord** : an internet cancer</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="../../favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href="https://crystal.tilde.institute/"> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title"><b><b>Discord</b></b> : an internet cancer</h1> -<div id="outline-container-org553a52a" class="outline-2"> -<h2 id="org553a52a">Preamble</h2> -<div class="outline-text-2" id="text-org553a52a"> -<p> -Before I start writing this article, I just want to clarify that I will NOT go over the technical aspect of <b><b>Discord</b></b> (such as the spyware and all) as it has been covered many times by other websites like <a href="https://spyware.neocities.org/articles/discord">This one !!!</a>, but basically, it’s exactly how you expect it to be, spying, selling data, monitoring open processes, terrible electron based app….etc -</p> - -<p> -I also wanted to make it clear that this is PURELY from my personal experience with <b><b>Discord</b></b> and the <b><b>Internet</b></b> as a whole, this isn’t an exact science and everybody can have an - although similar - different experience with the platform. Peace and love <3 -</p> -</div> -</div> -<div id="outline-container-org564e0f1" class="outline-2"> -<h2 id="org564e0f1">Chapter one : Curiosity</h2> -<div class="outline-text-2" id="text-org564e0f1"> -<p> -Picture yourself, it’s 2018/2019 and you are playing your favorite game, be it <b><b>Minecraft</b></b>, <b><b>League of Legends</b></b>, <b><b>CS:GO</b></b>, doesn’t matter. You start to play nicely, you make some friends, some enemies, typical gameplay. And then, one of them decides to take a step closer into your life, so they invite you to this cool new platform you have never heard about, <b><b>Discord</b></b>. Upon checking, you notice it’s a modern chat application for gamers…. “huh, must be nice” you might say. And then you are faced with a choice, you either create an account, or you don’t. -</p> - -<p> -If you decide to NOT make an account, you would be made fun of by that friend, or even get blamed for loses because “you weren’t in the voice chat”, you will be called a “Skype user”, probably miss out on events, giveaways, exclusive prizes and sometimes even get banned from that game server (Yeah, it happened on <b><b>Minecraft</b></b> before, failure to join the discord server actually rejects you from the Minecraft server). And even if we take a more…casual example, you found a cool piece of software online, but their guides and download links are all on <b><b>Discord</b></b>, or Discord exclusive, maybe you want to work with a team that solely use Discord. Basically you are missing out on a LOT. -</p> - -<p> -However, if you take the path of least resistance and decide to sign up, entering your e-mail address, password, birth date, and in the unfortunate case where you use a <b><b>VPN</b></b> or <b><b>TOR</b></b>, your phone number, pick a username and a profile picture. Congratulations, you now cursed yourself for the rest of your life. Remember that friend we imagined ? You play a few games together in VC, you crack jokes, you get to know each other… it’s all fun and games, but then, they send you a link you never saw before. Apparently it’s how you add people to groups in discord, they are called “Servers” -</p> - -<p> -> emkey.jpeg -</p> - -<p> -So you join that group they invited you to, it could be anything from a small friend group, to a large server with giveaways and events. But they all share one aspect, a hierarchy. -</p> -</div> -</div> -<div id="outline-container-org8d01749" class="outline-2"> -<h2 id="org8d01749">Chapter two : The hierarchy</h2> -<div class="outline-text-2" id="text-org8d01749"> -<p> -Now this hierarchy is not inherently bad, but this is how <b><b>Discord</b></b> (and even the communities on Discord) keep you addicted to them. When you join, you start as a peasant, a pleb, a noobie even. You have an ugly color for your username, and no access to “channels”, only few ones with cooldowns so you don’t talk much. And then you look at the members list, and you see a beautiful rainbow, people divided into categories, or roles as they like to call them!! -</p> - -<p> -At the top you will most likely find the Owner(s) or their loved ones, with colors that inspire majesty and fear, like a dark purple, these are the masters of the server, they shape it the way they want and in the rare occasion where they join the plebs in their discussions, they are met with rounds of applause. -</p> - -<p> -Then just below them you have the Right hand(s) of the owners, generally veterans and original members, they have a bright, warm yet still majestic color to their role. These have the same power as the Owners, but are more active in the server and are actually hated by a lot of users, who unfairly got banned or kicked. -</p> - -<p> -Then just below them you have the Bots, non-human, non-sentient beings, most of the time with a silvery metallic color as their username which are there to execute the Owners commands, or just to annoy the plebs, like a tax collector after a long day of work <b>“Congratulations you just advanced to level 5”</b> -</p> - -<p> -Now, you have the Moderators, these have some power, have an aggressive color as their role and are generally the ones who try to control the Chaos in the server, although most of the time they fail due to a lack of permissions, or threats from the Owners themselves. Regardless, these are the ones with the biggest ego, and most importantly they are the ones causing server splits. -</p> - -<p> -If the aforementioned roles are considered black, and normal users are white, then Helpers are definitely the gray line separating them. They are peasants who strive to go a rank higher, to be a majesty, and have some power. But most of the time, they are there for an eternity, or they just go from there all the way up to a Right hand using some witchcraft….Oh and their color is almost always Green :D -</p> - -<p> -After that we have the Plebeians which are also separated in an attempt to control them easily. But I’m going to go through the list quickly otherwise this article will take ages : you have the supporters - people who helped the server financially or in other ways -, partners which are just owners of other servers who decided to become living billboards, you have event winners to remind the others of what they can achieve if they wait long enough, then we have the activity roles, the more you are active, the more you have rights over casual users, this is definitely not a way to keep you addicted to the group discussion ;3 -</p> - -<p> -And finally, you have the outcasts, warned or muted people are all the way down the list, and they have little to no rights or uses in the server, quite frankly if they left they would have a better time !!!! -</p> - - -<p> -Okay so, in all seriousness. This at first glance doesn’t seem like a bad idea, after all you need order and laws in an easily accessible group. But this is not the way it’s used, this hierarchy is constantly there to remind you of what you can be if you are liked enough by the owners, what you can achieve. And in most cases, you get access to exclusive channels, a secret club, creating a sense of scarcity and power. This is bad because it keeps people invested in discussions they honestly don’t want nor need to have, but they are obliged, otherwise they are just a “powerless normie”. -</p> - -<p> -Now what happens if a Mod or an Owner decides to abuse their power ? Well in this case, here are the different outcomes : -</p> - -<ul class="org-ul"> -<li>Either people get angry and start spamming and protesting (usually ends with a purge or a mass ban)</li> -<li>People just blame the victim because it’s more profitable</li> -<li>An other rogue mod decides to take control and destroy the server</li> -<li>Or if it’s a disagreement between Owners, the server undergoes a split</li> -</ul> - - -<p> -If you are paying attention, you would know that all of these will always end with the same ending : “Another server gets created”, and so this is how… -</p> -</div> -</div> -<div id="outline-container-org4849802" class="outline-2"> -<h2 id="org4849802">Chapter three : <b><b>Discord</b></b> takes a once thriving community and splits it</h2> -<div class="outline-text-2" id="text-org4849802"> -<p> -Yes, there are always splits, and communities divide into multiple tiny sub-communities with their own opinions about useless matters. That is how you are kept invested. People love Drama, they love wars and they love picking sides. -</p> - -<p> -Let’s imagine together a simulation for what i mean, since i can’t draw or animate, use your imagination: -</p> -<ul class="org-ul"> -<li>You have a big red circle, its <b>Group A</b>, a pretty large tech community, with tiny dots inside with different colors, these are members and the colors represent their roles.</li> -<li>Once in a while, a fight happens in this group. Let’s say there is a fight between two normal users, a mod steps in and bans the user who is in the wrong. Not a big deal so far !</li> -<li>Now let’s imagine this scenario again, but with a different person, <b>Kevin</b>, a normal user in the group, but with a consistent presence, he is loved by a handful of people. Sadly he gets wrongly banned… wrong move for the mod, because now <b>Kevin</b> takes his supporters and make their own group, a blue one called <b>Group B</b></li> -<li><b>Group A</b>’s growth is starting to diminish because there is nothing to do there, and people are slowly moving to group <b>Group B</b> because of the overall aesthetic, in an attempt to win back their following, <b>Group A</b> decide to make events and reward their loyal followers. It kinda works but <b>Group B</b> is in a study growth</li> -<li>Oopsie, there is a minor disagreement between <b>Group A</b> owners, and it turns into a big war between them. which ends up with members taking sides and dividing the server in half, creating two new communities <b>Group C</b> and <b>Group D</b></li> -<li>And now, you know what is interesting ? is that all these 4 groups are not only semi-dead, but have the same users in them. AND SHARE THE SAME TOPIC</li> -</ul> - -<p> -So you basically killed a community, in 6 easy steps !!! And of course this will end up either by a mass deletion of these groups by a rogue Moderator, or a ban, or a screw up. So if the server contained important non-archived data. They are looong gone!!! -</p> -</div> -</div> -<div id="outline-container-orgb85fa6c" class="outline-2"> -<h2 id="orgb85fa6c">Chapter four : <b><b>Discord</b></b> users are NOT your friends</h2> -<div class="outline-text-2" id="text-orgb85fa6c"> -<p> -<b><b>Discord</b></b> is made in a way that makes it easy to get attached to people, and also really hard to get rid of them, because you share the same servers, same friends, and the border between Private talk and Public talk is really blurred. Not to mention how hard, if not impossible it is to find someone who you met before but lost their contact. Because not only could they change their tag, but there is no way to search their username, and the servers can disappear from a minute to an other, or go private, or anything really !!! Now <a href="http://shystudios.us/blog/discord/discord.html">Shy actually talked about this issue on their article about Discord,</a> but here I’m making a different point, in their article they say that it’s hard to get rid of someone you know via Discord, which is absolutely true. But it’s also easy to lost contact with someone literally in a split second, even people you deem “close” to you, they just…disappear!! So for y’all thinking about dating on Discord, that’s a terrible idea !!!! -Imagine you’re in a <b><b>Discord</b></b> server, vibing with some awesome people, chatting about everything from the latest memes to the mysteries of the universe. You’ve become practically inseparable online pals, sharing inside jokes and bonding over your mutual hatred for pineapple on pizza. Life is grand, right? -</p> - -<p> -But, brace yourself for the plot twist: <b><b>Discord</b></b> friendships are like a box of chocolates - you never know what you’re going to get. People appear and disappear from servers faster than you can say “dank meme.” One day, your best Discord buddy is there, cracking jokes and sharing dog pics, and the next day, poof, they’re gone. Maybe they got bored, maybe real life called, or maybe they wandered into the Discord Bermuda Triangle. Who knows? -</p> - -<p> -Now, here’s the kicker: finding a lost <b><b>Discord</b></b> friend is like trying to find a grain of sand on a beach during a hurricane. You can’t just Google them, and even if you know their username, it’s about as useful as a chocolate teapot if they’ve changed it. Servers vanish, go private, or morph faster than a Pokémon in a battle. It’s like trying to capture smoke with a butterfly net. -</p> - -<p> -So, for those pondering the idea of <b><b>Discord</b></b> romance, think twice! While forming connections is a breeze, keeping tabs on those connections is like herding cats in a hurricane! -</p> -</div> -</div> -<div id="outline-container-org77089c6" class="outline-2"> -<h2 id="org77089c6">Final Chapter : Login-walls</h2> -<div class="outline-text-2" id="text-org77089c6"> -<p> -People have made this point before and i will make it again, but locking important information behind a log-in page, with no way to find them using a Google search is stupid at best and manipulative at worst, because in this situation. Not only are you putting your faith on <b><b>Discord</b></b> servers to not fail one day, but on server Owners to not delete their work (and potentially rare unrecoverable work from other users). Not to mention that you actually need to be in that server to even know of the existence of these kind of resources. Regardless of how you see it, this is just putting valuable info in the hands of random people who could easily lock them behind a specific role that can be obtained either by paying, or by stroking their digital e-penis !!! -</p> - -<p> -You see, <b><b>Discord</b></b>, in all its infinite wisdom, believes it’s a brilliant idea to squirrel away precious knowledge behind a digital fortress that demands a username and password. It’s like saying, “Sure, I’ll share this life-changing information with you, but only if you can recall your umpteenth password!” -</p> - -<p> -Now, let’s break this down. First, you’re entrusting your prized data to <b><b>Discord</b></b> servers, which, let’s face it, are about as stable as a Jenga tower during an earthquake. One moment they’re there, and the next… poof! Gone with the wind. So much for your treasure trove of wisdom. -</p> - -<p> -And it gets even better. Server owners have the power to lock away valuable resources behind specific roles, which can be obtained through a combination of charm, flattery, or, heaven forbid, a cash transaction. It’s like saying, “Want to see the good stuff? Well, pony up or start groveling!” -</p> - -<p> -So, what’s the bottom line here? <b><b>Discord</b></b> has effectively become a modern-age Sphinx, guarding its secrets with a riddle of log-in screens. Your valuable info? In the hands of random folks who could decide to hoard it like misers guarding their gold or sell it to the highest bidder. It’s like a digital Wild West, and your information is the wild mustang everyone’s trying to wrangle. -</p> - -<p> -In conclusion, <b><b>Discord</b></b>’s penchant for login-walls is like locking away the Ark of the Covenant in a storage locker and hoping for the best. It’s the digital equivalent of hiding your keys in a haystack and hoping you can find them before the cows come home. -</p> -</div> -</div> -<div id="outline-container-orgc273b94" class="outline-2"> -<h2 id="orgc273b94">Conclusion</h2> -<div class="outline-text-2" id="text-orgc273b94"> -<p> -While <b><b>Discord</b></b> has its quirks and pitfalls, it’s essential to remember that it’s a reflection of the internet itself - a vast, ever-changing landscape filled with both wonder and peril. Your experience on Discord is uniquely yours, but it’s bound to be filled with surprises, friendships, and even the occasional drama. -</p> - -<p> -As we wrap up this exploration, it’s worth noting that <b><b>Discord</b></b>, like any digital space, is shaped by its users. The tales of adventures and misadventures, the rise and fall of servers, and the endless cycle of drama are all part of the grand tapestry of online life. -</p> - -<p> -So, if you find yourself lost in the labyrinthine corridors of <b><b>Discord</b></b> or stumble upon its peculiarities, remember, you’re not alone. Many have ventured before you, and many more will follow. The internet, after all, is an ever-evolving, enigmatic landscape where, as in life, every twist and turn holds the promise of a new adventure. -</p> - -<p> -If you ever have more anecdotes, insights, or questions to add to this digital saga, feel free to reach out. The story of <b><b>Discord</b></b> is far from over, and your voice could be the missing piece of the puzzle in this fascinating online journey. Until then, peace and love in your digital endeavors, and may your Discord adventures be filled with more joy than chaos! -</p> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2024-03-01 Fri 15:06</p> -</div> -</body> -</html> diff --git a/articles/feminism1_alex.html b/articles/feminism1_alex.html deleted file mode 100644 index 57e9271..0000000 --- a/articles/feminism1_alex.html +++ /dev/null @@ -1,92 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2023-11-10 Fri 21:45 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>Existing as a woman is a rebellion.</title> -<meta name="author" content="Alex" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="../../favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href="https://crystal.tilde.institute/"> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title">Existing as a woman is a rebellion.</h1> -<p> -<b>Original Link (You should def check it out):</b> -</p> - - - -<div id="org5add810" class="figure"> -<p><a href="https://gxrlhood.blogspot.com/2023/11/existing-as-woman-is-rebellion.html"><img src="https://crystal.tilde.institute/src/gifs/friend_banners/gay_gemstone.gif" alt="gay_gemstone.gif" /></a> -</p> -</div> -<div id="outline-container-org7548c76" class="outline-2"> -<h2 id="org7548c76">Original Article :</h2> -<div class="outline-text-2" id="text-org7548c76"> -<p class="verse"> -(Before starter, I want to note that I did make a tiny little mistake in my previous post, and I apologize for that! )<br /> -<br /> -What is a woman without a man? What is a free woman ? And can we affirm that women in our modern world are truly free?<br /> -<br /> -The simple act of existing freely as a woman is seen as a rebellion in this society, and by free I mean not basing her entire existence around men and how to please them.<br /> -<br /> -Women’s rights have been discussed for centuries, and are still an on going discussion excluding women themselves from it. (for instance: in Afghanistan, women don’t have the right for an education anymore, and in the United States, abortion is now illegal in some of the states.) We sexualise her, objectify her, we deprive her of her humanity and treat her like an animal. A woman is never seen as what she is and who is she, a simple human being.<br /> -<br /> -We could clearly see how much women are oppressed nowadays, if the world wasn’t purposefully blind. We shame them for enjoying their time on earth, we dismiss them, we silence them, we ruin them psychologically, We question their opinions, and their choices, we assault them, physically, verbally or both and blame them for it… These are just a few examples on how oppression towards women is still present.<br /> -<br /> -The women of the past fought for the ones of today, for them to have rights as human beings and to be free from oppression, and while the fruit of their efforts have payed, and gave women a better life, we still have a long way to go from finding true freedom. The assault that we face daily are just but one example out of many that men use to remind us of how much the world hates women, that the world we live in is still theirs, and that we are only viewed through their gaze.<br /> -<br /> -When I say men, I do mean all men. Even the ones who stays silent, especially the ones who stay silent. They maybe are not the ones assaulting but they surely are benefiting from the ones that do, so they certainly don’t condemn them. They are the ones questioning a woman’s sincerity, how many times did we hear statements such as « he would never do that », « he’s still my friend » and « it is none of my business »? This highlights how much a woman’s voice is muffled, and is questioned before being believed, and how little empathy men have towards the victims. They will also use the argument of fake accusation knowing very well that the statistic shows that less than 1% of the claims made by sexual assault victims are fake. Statistics also shows that one in three woman is victim of assault in her life, and that 98% of the assaulters are men. But they do not care about the statistics. In fact they are very well aware of the truth but choose to instead dismiss it.<br /> -<br /> -To respond clearly to the questions asked in the beginning: A woman without a man is simply a woman, a human being with a body and mind, with thoughts and ideas, with opinions and dreams, with urges,… just a simple human being.<br /> -<br /> -A free woman as of today, is a woman who doesn’t center her life around men, and thinks freely, she is provocative, affirm and validates her opinions, she is passionate about her dreams, she does not worry on how the world views her because she already knows, she is feared, because she has freed herself from the patriarchal and sexist ideas that the world has put into our minds.<br /> -<br /> -Unfortunately, women in this society are not free, their souls and bodies are still imprisoned in the very core of the patriarchy. Like I said earlier, men are going out of their ways to make sure the world is still theirs, and moreover, misogynistic behaviors are still present between women, since we have incorporated it so deeply in our lives, and in our way of thinking that it is easier for women to accept misogyny as the way of things than to question why we are so mean and cruel towards our own kind and notice the injustices.<br /> -<br /> -I could go on and on as to why women in this modern society are still oppressed, but I will only say this: to you dear reader, reading this essay (more a stream of consciousness than essay honestly) with knitted eyebrows and an angry face, open your eyes, and start seeing the world as it really is.<br /> -<br /> -To conclude, I do not think, I do not suppose, I do not express an opinion, I know, and I’m expressing facts, that the world is not ready to acknowledge.<br /> -<br /> -</p> -</div> -</div> -<div id="outline-container-org55509e4" class="outline-2"> -<h2 id="org55509e4">Webmaster’s response :</h2> -<div class="outline-text-2" id="text-org55509e4"> -<p> -While I do agree with mostly everything written above, I think there is much to add from multiple point of views and experiences, so I’m sharing mine here which, and following the general theme of the website, would be the technological aspect of being a women. -</p> - -<p> -When you first use the internet, you instantaneously assume that everyone is a man…I mean, that is one of the numerous rules of the web : <b>Rule 24: On the internet men are men, women are also men, and kids are undercover FBI agents</b>. Which is plain wrong, stupid, and sexist to a larger extent, assuming that women are not “smart enough” to be regular internet users. And this idea of course didn’t come from nowhere, i blame it mostly on American movies about “Tech-geeks” and all. But hey, we are not here to blame someone, just to notice! A lot of women are programmers, devs, cybersecurity experts, literal queens of the internet, yet a lot of people assume that women only use the internet to either bait you into buying their OnlyFans, or as a casual user, an easy to scam one too……Reminds you of something ? <b>smells like patriarchy</b> my dudes. -</p> - - -<p> -A lot of women, especially biological ones are seen as inferior programmers compared to biological men (I say biological men here, because it seems like cisgendered men prefer saying that a transfem is a better programmer than them, rather than saying that a WOMAN is better. Again, sexism down to the subatomic level) which, again, is not the case. And I know that from experience, one of the best Hackers I know is actually a girl!! -</p> - - -<p> -In the end, I think that no matter what we do, we won’t be able to change the image of the powerless skill-less woman that social media (and media in general) have created about women. So what should we do ? Should we go full Amish mode ? Or even do it Ted K style and ditch them all ? I will let you decide -</p> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Alex</p> -<p class="date">Created: 2023-11-10 Fri 21:45</p> -</div> -</body> -</html> \ No newline at end of file diff --git a/blog/asm/1.html b/blog/asm/1.html deleted file mode 100644 index 4ed3574..0000000 --- a/blog/asm/1.html +++ /dev/null @@ -1,538 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2024-04-10 Wed 21:05 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>x86 Assembly from my understanding</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="../../../favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href=""> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title">x86 Assembly from my understanding</h1> -<p> -Soooo this article (or maybe even a series of articles, who knows ?) will be about x86 assembly, or rather, what I understood from it and my road from the bottom-up hopefully reaching a good level of understanding -</p> -<div id="outline-container-orgd66d87f" class="outline-2"> -<h2 id="orgd66d87f">Memory :</h2> -<div class="outline-text-2" id="text-orgd66d87f"> -<p> -Memory is a sequence of octets (Aka 8bits) that each have a unique integer assigned to them called <b>The Effective Address (EA)</b>, in this particular CPU Architecture (the i8086), the octet is designated by a couple (A segment number, and the offset in the segment) -</p> - - -<ul class="org-ul"> -<li>The Segment is a set of 64 consecutive Koctets (1 Koctet = 1024 octets).</li> -<li>And the offset is to specify the particular octet in that segment.</li> -</ul> - -<p> -The offset and segment are encoded in 16bits, so they take a value between 0 and 65535 -</p> -</div> -<div id="outline-container-orgb9ec69c" class="outline-4"> -<h4 id="orgb9ec69c">Important :</h4> -<div class="outline-text-4" id="text-orgb9ec69c"> -<p> -The relation between the Effective Address and the Segment & Offset is as follow : -</p> - -<p> -<b><b>Effective address = 16 x segment + offset</b></b> keep in mind that this equation is encoded in decimal, which will change soon as we use Hexadecimal for convention reasons. -</p> -</div> -<ul class="org-ul"> -<li><a id="org407193f"></a>Example :<br /> -<div class="outline-text-5" id="text-org407193f"> -<p> -Let the Physical address (Or Effective Address, these two terms are interchangeable) <b>12345h</b> (the h refers to Hexadecimal, which can also be written like this <b>0x12345</b>), the register <b>DS = 1230h</b> and the register <b>SI = 0045h</b>, the CPU calculates the physical address by multiplying the content of the segment register <b>DS</b> by 10h (or 16) and adding the content of the register <b>SI</b>. so we get : <b>1230h x 10h + 45h = 12345h</b> -</p> - - -<p> -Now if you are a clever one ( I know you are, since you are reading this <3 ) you may say that the physical address <b>12345h</b> can be written in more than one way….and you are right, more precisely : <b>2<sup>12</sup> = 4096</b> different ways !!! -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-orgb81ab14" class="outline-3"> -<h3 id="orgb81ab14">Registers</h3> -<div class="outline-text-3" id="text-orgb81ab14"> -<p> -The 8086 CPU has 14 registers of 16bits of size. From the POV of the user, the 8086 has 3 groups of 4 registers of 16bits. One state register of 9bits and a counting program of 16bits inaccessible to the user (whatever this means). -</p> -</div> -<div id="outline-container-orgcd127f7" class="outline-4"> -<h4 id="orgcd127f7">General Registers</h4> -<div class="outline-text-4" id="text-orgcd127f7"> -<p> -General registers contribute to arithmetic’s and logic and addressing too. -</p> - - -<p> -Each half-register is accessible as a register of 8bits, therefor making the 8086 backwards compatible with the 8080 (which had 8bit registers) -</p> - - -<p> -Now here are the Registers we can find in this section: -</p> - - -<p> -<b>AX</b>: This is the accumulator. It is of 16 bits and is divided into two 8-bit registers AH and AL to also perform 8-bit instructions. It is generally used for arithmetical and logical instructions but in 8086 microprocessor it is not mandatory to have an accumulator as the destination operand. Example: -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">ADD</span> <span style="color: #cba6f7;">AX</span>, AX <span style="color: #6c7086;">;</span><span style="color: #6c7086;">(AX = AX + AX)</span> -</pre> -</div> - -<p> -<b>BX</b>: This is the base register. It is of 16 bits and is divided into two 8-bit registers BH and BL to also perform 8-bit instructions. It is used to store the value of the offset. Example: -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">BL</span>, [<span style="color: #fab387;">500</span>] <span style="color: #6c7086;">;</span><span style="color: #6c7086;">(BL = 500H)</span> -</pre> -</div> - -<p> -<b>CX</b>: This is the counter register. It is of 16 bits and is divided into two 8-bit registers CH and CL to also perform 8-bit instructions. It is used in looping and rotation. Example: -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">CX</span>, <span style="color: #fab387;">0005</span> -<span style="color: #89b4fa;">LOOP</span> -</pre> -</div> - -<p> -<b>DX</b>: This is the data register. It is of 16 bits and is divided into two 8-bit registers DH and DL to also perform 8-bit instructions. It is used in the multiplication and input/output port addressing. Example: -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">MUL</span> <span style="color: #cba6f7;">BX</span> (DX, AX = AX * BX) -</pre> -</div> -</div> -</div> -</div> -<div id="outline-container-orgde83b9e" class="outline-3"> -<h3 id="orgde83b9e">Addressing and registers…again</h3> -<div class="outline-text-3" id="text-orgde83b9e"> -</div> -<div id="outline-container-org598f23b" class="outline-4"> -<h4 id="org598f23b">I realized what I wrote here before was almost gibberish, sooo here we go again I guess ?</h4> -<div class="outline-text-4" id="text-org598f23b"> -<p> -Well lets take a step back to the notion of effective addresses VS relative ones. -</p> -</div> -</div> -<div id="outline-container-orga54d5c9" class="outline-4"> -<h4 id="orga54d5c9">Effective = 10h x Segment + Offset . Part1</h4> -<div class="outline-text-4" id="text-orga54d5c9"> -<p> -When trying to access a specific memory space, we use this annotation <b>[Segment:Offset]</b>, so for example, and assuming <b>DS = 0100h</b>. We want to write the value <b>0x0005</b> to the memory space defined by the physical address <b>1234h</b>, what do we do ? -</p> -</div> -<ul class="org-ul"> -<li><a id="org330429e"></a>Answer :<br /> -<div class="outline-text-5" id="text-org330429e"> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">MOV</span> [DS:0234h], 0x0005 -</pre> -</div> - -<p> -Why ? Let’s break it down : -</p> - - - -<div id="orge9d2dab" class="figure"> -<p><img src="../../src/gifs/lain-dance.gif" alt="lain-dance.gif" /> -</p> -</div> - - -<p> -We Already know that <b>Effective = 10h x Segment + Offset</b>, So here we have : <b>1234h = 10h x DS + Offset</b>, we already know that <b>DS = 0100h</b>, we end up with this simple equation <b>1234h = 1000h + Offset</b>, therefor the Offset is <b>0234h</b> -</p> - - -<p> -Simple, right ?, now for another example -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org21257b6" class="outline-4"> -<h4 id="org21257b6">Another example :</h4> -<div class="outline-text-4" id="text-org21257b6"> -<p> -What if we now have this instruction ? -</p> -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">MOV</span> [0234h], 0x0005 -</pre> -</div> -<p> -What does it do ? You might or might not be surprised that it does the exact same thing as the other snipped of code, why though ? Because apparently and for some odd reason I don’t know, the compiler Implicitly assumes that the segment used is the <b>DS</b> one. So if you don’t specify a register( we will get to this later ), or a segment. Then the offset is considered an offset with a DS segment. -</p> -</div> -</div> -<div id="outline-container-org7c948b1" class="outline-4"> -<h4 id="org7c948b1">Segment + Register <3</h4> -<div class="outline-text-4" id="text-org7c948b1"> -<p> -Consider <b>DS = 0100h</b> and <b>BX = BP = 0234h</b> and this code snippet: -</p> -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">MOV</span> [BX], 0x0005 <span style="color: #6c7086;">; </span><span style="color: #a6e3a1; font-weight: bold;">NOTE</span><span style="color: #6c7086;"> : ITS NOT THE SAME AS MOV BX, 0x0005. Refer to earlier paragraphs</span> -</pre> -</div> - - -<p> -Well you guessed it right, it also does the same thing, but now consider this : -</p> -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">MOV</span> [BP], 0x0005 -</pre> -</div> - -<p> -If you answered that its the same one, you are wrong. And this is because the segment used changes according to the offset as I said before in an implicit way. Here is the explicit equivalent of the two commands above: -</p> -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">MOV</span> [DS:BX], 0x0005 - <span style="color: #cba6f7;">MOV</span> [SS:BP], 0x0005 -</pre> -</div> - -<p> -The General rule of thumb is as follows : -</p> -<ul class="org-ul"> -<li>If the offset is : DI SI or BX, the Segment used is DS.</li> -<li>If its BP or SP, then the segment is SS.</li> -</ul> -</div> -<ul class="org-ul"> -<li><a id="orgec605fb"></a>Note<br /> -<div class="outline-text-5" id="text-orgec605fb"> -<p> -The values of the registers CS DS and SS are automatically initialized by the OS when launching the program. So these segments are implicit. AKA : If we want to access a specific data in memory, we just need to specify its offset. Also you can’t write directly into the DS or CS segment registers, so something like -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">DS</span>, 0x0005 <span style="color: #6c7086;">; </span><span style="color: #6c7086;">Is INVALID</span> -<span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">DS</span>, AX <span style="color: #6c7086;">; </span><span style="color: #6c7086;">This one is VALID</span> -</pre> -</div> -</div> -</li> -</ul> -</div> -</div> -</div> -<div id="outline-container-org30acf72" class="outline-2"> -<h2 id="org30acf72">The ACTUAL thing :</h2> -<div class="outline-text-2" id="text-org30acf72"> -<p> -Enough technical rambling, and now we shall go to the fun part, the ACTUAL CODE. But first, some names you should be familiar with : -</p> - -<ul class="org-ul"> -<li><b>Mnemonics</b> : Or <b>Instructions</b>, are the…well…Instructions executed by the CPU like <b>MOV</b> , <b>ADD</b>, <b>MUL</b>…etc, they are case <b>insensitive</b> but i like them better in UPPERCASE.</li> -<li><b>Operands</b> : These are the options passed to the instructions, like <b>MOV dst, src</b>, and they can be anything from a memory location, to a variable to an immediate address.</li> -</ul> -</div> -<div id="outline-container-org03a7d0f" class="outline-3"> -<h3 id="org03a7d0f">Structure of an assembly program :</h3> -<div class="outline-text-3" id="text-org03a7d0f"> -<p> -While there is no “standard” structure, i prefer to go with this one : -</p> - -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">org</span> 100h -<span style="color: #cba6f7;">.data</span> - <span style="color: #6c7086;">; </span><span style="color: #6c7086;">variables and constants</span> - -<span style="color: #cba6f7;">.code</span> - <span style="color: #6c7086;">; </span><span style="color: #6c7086;">instructions</span> -</pre> -</div> -</div> -</div> -<div id="outline-container-orgbea80df" class="outline-3"> -<h3 id="orgbea80df">MOV dst, src</h3> -<div class="outline-text-3" id="text-orgbea80df"> -<p> -The MOV instruction copies the Second operand (src) to the First operand (dst)… The source can be a memory location, an immediate value, a general-purpose register (AX BX CX DX). As for the Destination, it can be a general-purpose register or a memory location. -</p> - - -<p> -these types of operands are supported: -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">REG</span>, memory -<span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">memory</span>, REG -<span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">REG</span>, REG -<span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">memory</span>, immediate -<span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">REG</span>, immediate -</pre> -</div> -<p> -<b>REG</b>: AX, BX, CX, DX, AH, AL, BL, BH, CH, CL, DH, DL, DI, SI, BP, SP. -</p> - -<p> -<b>memory</b>: [BX], [BX+SI+7], variable -</p> - -<p> -<b>immediate</b>: 5, -24, 3Fh, 10001101b -</p> - - -<p> -for segment registers only these types of MOV are supported: -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">SREG</span>, memory -<span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">memory</span>, SREG -<span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">REG</span>, SREG -<span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">SREG</span>, REG -<span style="color: #89b4fa;">SREG</span>: <span style="color: #cba6f7;">DS</span>, ES, SS, and only as second operand: CS. -</pre> -</div> -<p> -<b>REG</b>: AX, BX, CX, DX, AH, AL, BL, BH, CH, CL, DH, DL, DI, SI, BP, SP. -</p> - -<p> -<b>memory</b>: [BX], [BX+SI+7], variable -</p> -</div> -<div id="outline-container-orge229cf5" class="outline-4"> -<h4 id="orge229cf5">Note : The MOV instruction <b>cannot</b> be used to set the value of the CS and IP registers</h4> -</div> -</div> -<div id="outline-container-org05f299b" class="outline-3"> -<h3 id="org05f299b">Variables :</h3> -<div class="outline-text-3" id="text-org05f299b"> -<p> -Let’s say you want to use a specific value multiple times in your code, do you prefer to call it using something like <b>var1</b> or <b>E4F9:0011</b> ? If your answer is the second option, you can gladly skip this section, or even better, seek therapy. -</p> - -<p> -Anyways, we have two types of variables, <b>bytes</b> and <b>words(which are two bytes)</b>, and to define a variable, we use the following syntax -</p> - -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">name</span> <span style="color: #cba6f7;">DB</span> value <span style="color: #6c7086;">; </span><span style="color: #6c7086;">To Define a Byte</span> -<span style="color: #89b4fa;">name</span> <span style="color: #cba6f7;">DW</span> value <span style="color: #6c7086;">; </span><span style="color: #6c7086;">To Define a Word</span> -</pre> -</div> - -<p> -<b>name</b> - can be any letter or digit combination, though it should start with a letter. It’s possible to declare unnamed variables by not specifying the name (this variable will have an address but no name). -<b>value</b> - can be any numeric value in any supported numbering system (hexadecimal, binary, or decimal), or “?” symbol for variables that are not initialized. -</p> -</div> -<div id="outline-container-orga473d7b" class="outline-4"> -<h4 id="orga473d7b">Example code :</h4> -<div class="outline-text-4" id="text-orga473d7b"> -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">org</span> 100h - <span style="color: #cba6f7;">.data</span> - <span style="color: #cba6f7;">x</span> db <span style="color: #fab387;">33</span> - <span style="color: #cba6f7;">y</span> dw 1350h - - <span style="color: #cba6f7;">.code</span> - <span style="color: #cba6f7;">MOV</span> AL, x - <span style="color: #cba6f7;">MOV</span> BX, y -</pre> -</div> -</div> -</div> -<div id="outline-container-org8ceedbb" class="outline-4"> -<h4 id="org8ceedbb">Arrays :</h4> -<div class="outline-text-4" id="text-org8ceedbb"> -<p> -We can also define Arrays instead of single values using comma separated vaues. like this for example -</p> -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">a</span> db 48h, 65h, 6Ch, 6Fh, 00H - <span style="color: #cba6f7;">b</span> db 'Hello', <span style="color: #fab387;">0</span> -</pre> -</div> - -<p> -Surprise Surprise, the arrays a and b are identical, the reason behind it is that characters are first converted to their ASCII values then stored in memory!!! Wonderful right ? And guess what, accessing values in assembly IS THE SAME AS IN C !!! -</p> -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">MOV</span> AL, a[<span style="color: #fab387;">0</span>] <span style="color: #6c7086;">; </span><span style="color: #6c7086;">Copies 48h to AL</span> - <span style="color: #cba6f7;">MOV</span> BL, b[<span style="color: #fab387;">0</span>] <span style="color: #6c7086;">; </span><span style="color: #6c7086;">Also Copies 48h to BL</span> -</pre> -</div> -<p> -You can also use any of the memory index registers BX, SI, DI, BP, for example: -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">SI</span>, <span style="color: #fab387;">3</span> -<span style="color: #89b4fa;">MOV</span> <span style="color: #cba6f7;">AL</span>, a[SI] -</pre> -</div> - -<p> -If you need to declare a large array you can use DUP operator. -The syntax for <b>DUP</b>: -</p> - -<p> -number DUP ( value(s) ) -<b>number</b> - number of duplicate to make (any constant value). -<b>value</b> - expression that DUP will duplicate. -</p> - -<p> -for example: -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">c</span> <span style="color: #cba6f7;">DB</span> <span style="color: #fab387;">5</span> DUP(<span style="color: #fab387;">9</span>) -<span style="color: #6c7086;">;</span><span style="color: #6c7086;">is an alternative way of declaring:</span> -<span style="color: #89b4fa;">c</span> <span style="color: #cba6f7;">DB</span> <span style="color: #fab387;">9</span>, <span style="color: #fab387;">9</span>, <span style="color: #fab387;">9</span>, <span style="color: #fab387;">9</span>, <span style="color: #fab387;">9</span> -</pre> -</div> -<p> -one more example: -</p> -<div class="org-src-container"> -<pre class="src src-asm"><span style="color: #89b4fa;">d</span> <span style="color: #cba6f7;">DB</span> <span style="color: #fab387;">5</span> DUP(<span style="color: #fab387;">1</span>, <span style="color: #fab387;">2</span>) -<span style="color: #6c7086;">;</span><span style="color: #6c7086;">is an alternative way of declaring:</span> -<span style="color: #89b4fa;">d</span> <span style="color: #cba6f7;">DB</span> <span style="color: #fab387;">1</span>, <span style="color: #fab387;">2</span>, <span style="color: #fab387;">1</span>, <span style="color: #fab387;">2</span>, <span style="color: #fab387;">1</span>, <span style="color: #fab387;">2</span>, <span style="color: #fab387;">1</span>, <span style="color: #fab387;">2</span>, <span style="color: #fab387;">1</span>, <span style="color: #fab387;">2</span> -</pre> -</div> -<p> -Of course, you can use DW instead of DB if it’s required to keep values larger then 255, or smaller then -128. DW cannot be used to declare strings. -</p> -</div> -</div> -<div id="outline-container-org8fefb4b" class="outline-4"> -<h4 id="org8fefb4b">LEA</h4> -<div class="outline-text-4" id="text-org8fefb4b"> -<p> -LEA stands for (Load Effective Address) is an instruction used to get the offset of a specific variable. We will see later how its used, but first. here is something we will need : -</p> - -<p> -In order to tell the compiler about data type, -these prefixes should be used: -</p> - -<p> -<b>BYTE PTR</b> - for byte. -<b>WORD PTR</b> - for word (two bytes). -</p> - -<p> -For example: -<b>BYTE PTR [BX]</b> ; byte access. - or -<b>WORD PTR [BX]</b> ; word access. -assembler supports shorter prefixes as well: -</p> - -<ul class="org-ul"> -<li>b. - for BYTE PTR</li> -<li>w. - for WORD PTR</li> -</ul> - -<p> -in certain cases the assembler can calculate the data type automatically. -</p> -</div> -<ul class="org-ul"> -<li><a id="orgd644e48"></a>Example :<br /> -<div class="outline-text-5" id="text-orgd644e48"> -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">org</span> 100h - <span style="color: #cba6f7;">.data</span> - <span style="color: #cba6f7;">VAR1</span> db 50h - <span style="color: #cba6f7;">VAR2</span> dw 1234h - <span style="color: #cba6f7;">.code</span> - <span style="color: #cba6f7;">MOV</span> AL, VAR1 <span style="color: #6c7086;">; </span><span style="color: #6c7086;">We check the value of VAR1 by putting it in AL</span> - <span style="color: #cba6f7;">MOV</span> AX, VAR2 <span style="color: #6c7086;">; </span><span style="color: #6c7086;">Same here</span> - <span style="color: #cba6f7;">LEA</span> BX, VAR1 <span style="color: #6c7086;">; </span><span style="color: #6c7086;">BX receives the Address of VAR1</span> - <span style="color: #cba6f7;">MOV</span> b.[BX], 44h - <span style="color: #cba6f7;">MOV</span> AL, VAR1 <span style="color: #6c7086;">; </span><span style="color: #6c7086;">We effectively changed the content of the VAR1 variable</span> - <span style="color: #cba6f7;">LEA</span> BX, VAR2 - <span style="color: #cba6f7;">MOV</span> w.[BX], 5678h - <span style="color: #cba6f7;">MOV</span> AX, VAR2 -</pre> -</div> -</div> -</li> -</ul> -</div> -<div id="outline-container-org99559c2" class="outline-4"> -<h4 id="org99559c2">Constants :</h4> -<div class="outline-text-4" id="text-org99559c2"> -<p> -Constants in Assembly only exist until the code is assembled, meaning that if you disassemble your code later, you wont see your constant definitions. -</p> - -<p> -Defining constants is pretty straight forward : -</p> -<div class="org-src-container"> -<pre class="src src-asm"> <span style="color: #cba6f7;">name</span> EQU value -</pre> -</div> - -<p> -Of course constants cant be changed, and aren’t stored in memory. So they are like little macros that live in your code. -</p> -</div> -</div> -</div> -<div id="outline-container-org9179f72" class="outline-3"> -<h3 id="org9179f72">⚐ :</h3> -<div class="outline-text-3" id="text-org9179f72"> -<p> -Now comes the notion of <b>Flags</b>, which are bits in the <b>Status register</b>, which are used for logical and arithmetical instructions and can take a value of 1 or 0 . Here are the 8 flags that exist for the 8086 CPU : -</p> -<ul class="org-ul"> -<li><b>Carry Flag(CF):</b> Set to 1 when there is an <b>unsigned overflow</b>, for example when you add 255 + 1( not in range [0,255] ). by default its set to 0.</li> -<li><b>Overflow Flag(CF):</b> Set to 1 when there is a <b>signed overflow</b>, for example when you add 100 + 50( not in range [-128, 128[ ). by default its set to 0.</li> -<li><b>Zero Flag(ZF):</b> Set to 1 when the result is 0. by default its set to 0.</li> -<li><b>Auxiliary Flag(AF):</b> Set to 1 when there is an <b>unsigned overflow</b> for low nibble (4bits), or in human words : when there is a carry inside the number. for example when you add 29H + 4CH , 9 + C => 15. So we carry the 1 to 2 + 4 and AF is set to 1.</li> -<li><b>Parity Flag(PF):</b> Set to 1 when the result has an even number of one bits. and 0 if it has an odd number of one bits. Even if a result is a word, only the Low 8bits are analyzed.</li> -<li><b>Sign Flag(SF):</b> Self explanatory, set to 1 if the result is negative and 0 if its positive.</li> -<li><b>Interrupt Enable Flag(IF):</b> When its set to 1, the CPU reacts to interrupts from external devices.</li> -<li><b>Direction Flag(DF):</b> When this flag is set to 0, the processing is done forward, if its set to 1, its done backward.</li> -</ul> -</div> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2024-04-10 Wed 21:05</p> -</div> -</body> -</html> diff --git a/blog/c/cherry.html b/blog/c/cherry.html deleted file mode 100644 index e2d9221..0000000 --- a/blog/c/cherry.html +++ /dev/null @@ -1,171 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2024-03-17 Sun 21:46 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>Reviving Caesar with a Cherry-flavored Crystal</title> -<meta name="author" content="Crystal & Sloth" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="../../../favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href=""> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title">Reviving Caesar with a Cherry-flavored Crystal</h1> -<div id="outline-container-org0bff230" class="outline-2"> -<h2 id="org0bff230">What ?…</h2> -<div class="outline-text-2" id="text-org0bff230"> -<p> -That is probably your reaction reading this title, and no, this isn’t a randomly generated sentence, but rather a simple encryption algorithm I recently made (Actually the first encryption algorithm i make at all!!). Meet <b>Cherry-Crystal Encryption</b>. -</p> -</div> -</div> -<div id="outline-container-org4770304" class="outline-2"> -<h2 id="org4770304">Okay so, what is this all about ?</h2> -<div class="outline-text-2" id="text-org4770304"> -<p> -This encryption Algorithm that we will call <b>CCE</b> for short, takes inspiration from the Caesar cipher which needn’t an introduction (you can find great explanations online). But what about mine you might ask ? -</p> - - -<ul class="org-ul"> -<li>It’s actually pretty simple. We start with a <b>Cherry</b> or a <b>Visible phrase</b>, or a <b>Decoy</b>, that we will share to people who we don’t want to know the secret phrase..</li> -<li>Then we ask the user to enter their <b>Crystal</b>, <b>invisible phrase</b> or <b>secret</b>.</li> -<li>The program then outputs an array of Integers called the <b>Mask</b>, or the <b>Shift</b>. That is, the shift required to go from cherry<sub>i</sub> to crystal<sub>i</sub>.</li> -<li>Finally, we use both the <b>Cherry</b> and <b>Mask</b> to get the <b>Crystal</b>, a single missing number or letter from both of them can and will output rubbish content.</li> -</ul> -</div> -</div> -<div id="outline-container-org4496ca5" class="outline-2"> -<h2 id="org4496ca5">The Code :</h2> -<div class="outline-text-2" id="text-org4496ca5"> -<div class="org-src-container"> -<pre class="src src-c"><span style="color: #f9e2af;">#include</span> <span style="color: #f38ba8;"><</span><span style="color: #a6e3a1;">stdio.h</span><span style="color: #f38ba8;">></span> -<span style="color: #f9e2af;">#include</span> <span style="color: #f38ba8;"><</span><span style="color: #a6e3a1;">stdlib.h</span><span style="color: #f38ba8;">></span> -<span style="color: #f9e2af;">#include</span> <span style="color: #f38ba8;"><</span><span style="color: #a6e3a1;">string.h</span><span style="color: #f38ba8;">></span> - -<span style="color: #f9e2af;">void</span> <span style="color: #89b4fa;">sloth</span><span style="color: #f38ba8;">(</span><span style="color: #f9e2af;">char</span> <span style="color: #cdd6f4;">cherry</span><span style="color: #fab387;">[]</span>, <span style="color: #f9e2af;">char</span> <span style="color: #cdd6f4;">crystal</span><span style="color: #fab387;">[]</span>, <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">mask</span><span style="color: #fab387;">[]</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> - <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">i</span>; - <span style="color: #cba6f7;">for</span> <span style="color: #fab387;">(</span>i = <span style="color: #fab387;">0</span>; i < strlen<span style="color: #f9e2af;">(</span>cherry<span style="color: #f9e2af;">)</span> - <span style="color: #fab387;">1</span>; i++<span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> - mask<span style="color: #f9e2af;">[</span>i<span style="color: #f9e2af;">]</span> = cherry<span style="color: #f9e2af;">[</span>i<span style="color: #f9e2af;">]</span> - crystal<span style="color: #f9e2af;">[</span>i<span style="color: #f9e2af;">]</span>; - <span style="color: #fab387;">}</span> - <span style="color: #cba6f7;">for</span> <span style="color: #fab387;">(</span>i = strlen<span style="color: #f9e2af;">(</span>cherry<span style="color: #f9e2af;">)</span> - <span style="color: #fab387;">1</span>; i < strlen<span style="color: #f9e2af;">(</span>crystal<span style="color: #f9e2af;">)</span> - <span style="color: #fab387;">1</span>; i++<span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> - mask<span style="color: #f9e2af;">[</span>i<span style="color: #f9e2af;">]</span> = crystal<span style="color: #f9e2af;">[</span>i<span style="color: #f9e2af;">]</span>; - <span style="color: #fab387;">}</span> -<span style="color: #f38ba8;">}</span> -<span style="color: #f9e2af;">void</span> <span style="color: #89b4fa;">moon</span><span style="color: #f38ba8;">(</span><span style="color: #f9e2af;">char</span> <span style="color: #cdd6f4;">cherry</span><span style="color: #fab387;">[]</span>, <span style="color: #f9e2af;">char</span> <span style="color: #cdd6f4;">crystal</span><span style="color: #fab387;">[]</span>, <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">mask</span><span style="color: #fab387;">[]</span>, <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">length</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> - <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">i</span>, <span style="color: #cdd6f4;">end</span> = <span style="color: #fab387;">1</span>; - <span style="color: #cba6f7;">for</span> <span style="color: #fab387;">(</span>i = <span style="color: #fab387;">0</span>; i < length; i++<span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> - <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>i == strlen<span style="color: #a6e3a1;">(</span>cherry<span style="color: #a6e3a1;">)</span> - <span style="color: #fab387;">1</span> || end == <span style="color: #fab387;">0</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> - crystal<span style="color: #a6e3a1;">[</span>i<span style="color: #a6e3a1;">]</span> = mask<span style="color: #a6e3a1;">[</span>i<span style="color: #a6e3a1;">]</span>; - end = <span style="color: #fab387;">0</span>; - <span style="color: #f9e2af;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #f9e2af;">{</span> - crystal<span style="color: #a6e3a1;">[</span>i<span style="color: #a6e3a1;">]</span> = cherry<span style="color: #a6e3a1;">[</span>i<span style="color: #a6e3a1;">]</span> - mask<span style="color: #a6e3a1;">[</span>i<span style="color: #a6e3a1;">]</span>; - <span style="color: #f9e2af;">}</span> - <span style="color: #fab387;">}</span> -<span style="color: #f38ba8;">}</span> -<span style="color: #f9e2af;">int</span> <span style="color: #89b4fa;">main</span><span style="color: #f38ba8;">(</span><span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">argc</span>, <span style="color: #f9e2af;">char</span> *<span style="color: #cdd6f4;">argv</span><span style="color: #fab387;">[]</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> - <span style="color: #cba6f7;">const</span> <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">size</span> = <span style="color: #fab387;">1028</span>; - <span style="color: #f9e2af;">char</span> <span style="color: #cdd6f4;">cherry</span><span style="color: #fab387;">[</span>size<span style="color: #fab387;">]</span>, <span style="color: #cdd6f4;">cherry2</span><span style="color: #fab387;">[</span>size<span style="color: #fab387;">]</span>, <span style="color: #cdd6f4;">crystal</span><span style="color: #fab387;">[</span>size<span style="color: #fab387;">]</span>, <span style="color: #cdd6f4;">crystal2</span><span style="color: #fab387;">[</span>size<span style="color: #fab387;">]</span>; - <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">mask</span><span style="color: #fab387;">[</span>size<span style="color: #fab387;">]</span>, <span style="color: #cdd6f4;">mask2</span><span style="color: #fab387;">[</span>size<span style="color: #fab387;">]</span>, <span style="color: #cdd6f4;">i</span>; - <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">length</span> = <span style="color: #fab387;">0</span>; - puts<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Enter the Cherry: "</span><span style="color: #fab387;">)</span>; - fgets<span style="color: #fab387;">(</span>cherry, size, stdin<span style="color: #fab387;">)</span>; - puts<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Enter the Crystal: "</span><span style="color: #fab387;">)</span>; - fgets<span style="color: #fab387;">(</span>crystal, size, stdin<span style="color: #fab387;">)</span>; - sloth<span style="color: #fab387;">(</span>cherry, crystal, mask<span style="color: #fab387;">)</span>; - <span style="color: #cba6f7;">for</span> <span style="color: #fab387;">(</span>i = <span style="color: #fab387;">0</span>; i < strlen<span style="color: #f9e2af;">(</span>crystal<span style="color: #f9e2af;">)</span> - <span style="color: #fab387;">1</span>; i++<span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> - printf<span style="color: #f9e2af;">(</span><span style="color: #a6e3a1;">"%d "</span>, mask<span style="color: #a6e3a1;">[</span>i<span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span>; - length++; - <span style="color: #fab387;">}</span> - printf<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"\nYour mask is : %d characters long"</span>, length<span style="color: #fab387;">)</span>; - puts<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"\n===Decryption: ===\n"</span><span style="color: #fab387;">)</span>; - puts<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Enter the Cherry: "</span><span style="color: #fab387;">)</span>; - fgets<span style="color: #fab387;">(</span>cherry2, size, stdin<span style="color: #fab387;">)</span>; - puts<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Enter the size of the Mask: "</span><span style="color: #fab387;">)</span>; - scanf<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"%d"</span>, &length<span style="color: #fab387;">)</span>; - puts<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Enter the mask: "</span><span style="color: #fab387;">)</span>; - <span style="color: #cba6f7;">for</span> <span style="color: #fab387;">(</span>i = <span style="color: #fab387;">0</span>; i < length; i++<span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> - scanf<span style="color: #f9e2af;">(</span><span style="color: #a6e3a1;">"%d"</span>, &mask2<span style="color: #a6e3a1;">[</span>i<span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span>; - <span style="color: #fab387;">}</span> - puts<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"The Crystal is: "</span><span style="color: #fab387;">)</span>; - moon<span style="color: #fab387;">(</span>cherry2, crystal2, mask2, length<span style="color: #fab387;">)</span>; - puts<span style="color: #fab387;">(</span>crystal2<span style="color: #fab387;">)</span>; - <span style="color: #cba6f7;">return</span> <span style="color: #fab387;">0</span>; -<span style="color: #f38ba8;">}</span> - -</pre> -</div> - -<p> -The program has been tested both on Alpine OS with Musl libc (thanks <a href="https://kaa.neocities.org/">Kin</a>) and on OpenBSD 7.5-current. In the close future I will make a git repo as i’m planning to upgrade it and just make it better overall, who knows, maybe i will make a library out of it!! -</p> -</div> -</div> -<div id="outline-container-org6c3305a" class="outline-2"> -<h2 id="org6c3305a">How does it work ?</h2> -<div class="outline-text-2" id="text-org6c3305a"> -</div> -<div id="outline-container-orgf462a7c" class="outline-3"> -<h3 id="orgf462a7c">Slothing (Encrypting) 🦥:</h3> -<div class="outline-text-3" id="text-orgf462a7c"> -<p> -<del>What is it with these names I pick ?</del> Anyways, the <b>sloth(char *cherry, char *crystal, int *mask)</b> void function takes as parameters three variables: -</p> - -<ul class="org-ul"> -<li>A pointer to a <b>char array</b> or simply said <b>a string</b>, It’s the <b>Cherry</b>.</li> -<li>Another pointer to the <b>Crystal</b>.</li> -<li>And Finally, a pointer to an array of integers <b>The Mask</b> which will be output-ed by the function.</li> -</ul> - - -<p> -The general idea of it is like this : (we will use a quick example) -</p> - -<ul class="org-ul"> -<li><b>Cherry</b>: H e l l o \0.</li> -<li><b>Crystal</b>: W o r l d \0.</li> -<li>Cherry[0] here is <b>H</b>, or in ASCII <b>72</b>. And Crystal[0] is <b>W</b> or <b>87</b>.</li> -<li>Mask[0] in this case is : Cherry[0] - Crystal[0]. which is <b>-15</b>. We then repeat the same steps for each letter on the <b>Crystal</b>.</li> -</ul> - -<p> -Why the emphasis on <b>Crystal</b> ? Because we might end up with a case of a Crystal larger than a Cherry. we set the offset to the ASCII value of <b>Crystal[i]</b>, okay which to be fair is not the safest option out there, but I’m planning on fixing it sooner or later. In the case of a large Cherry but a small Crystal…it works but now looking at the code, i have no idea why it works the intended way…. -</p> -</div> -</div> -<div id="outline-container-org7cb73ea" class="outline-3"> -<h3 id="org7cb73ea">Mooning (Decrypting) 🌕:</h3> -<div class="outline-text-3" id="text-org7cb73ea"> -<p> -The function <b>moon(char *cherry, char *crystal, int *mask, int length)</b> works the same way as the sloth function, but in reverse and a small change. -</p> - -<ul class="org-ul"> -<li><b>The for loop goes through all the elements of the Mask and reconstructing the Crystal using the reverse equation of the encryption</b>. But when it arrives at the end of the <b>Cherry</b> (here we enter the case of a Cherry smaller than a Crystal). Then we will just assume that <b>Mask[i]</b> is the ASCII code of <b>Crystal[i]</b>, and we continue this assumption until the end of the loop.</li> -</ul> - - -<p> -And voila that’s it. Of course there might be some things I will change, but the overall concept is here! -</p> -</div> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal & Sloth</p> -<p class="date">Created: 2024-03-17 Sun 21:46</p> -</div> -</body> -</html> diff --git a/blog/c/game.html b/blog/c/game.html deleted file mode 100644 index 90c1965..0000000 --- a/blog/c/game.html +++ /dev/null @@ -1,346 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2024-02-22 Thu 19:09 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>The loneliness Game</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="../../../favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href=""> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title">The loneliness Game</h1> -<p> -Hello !!, I hope you are doing great you amazing person whoever you are, and I really appreciate you reading my little C programming adventure. Soo basically I wanted to blog about a little game I made when bored, and figured out it would be a great way to optimize it, and learn new stuff too by documenting the process! -</p> -<div id="outline-container-org26dcb46" class="outline-2"> -<h2 id="org26dcb46">The concept :</h2> -<div class="outline-text-2" id="text-org26dcb46"> -<p> -Basically the player is faced with a NxM field made up with the sign <b>“-”</b> and the player is denoted by the symbol <b>“+”</b>, there are also Bonuses <b>“B”</b> which add 1 to your score, Traps <b>“T”</b>, that remove one from your score, and Dead <b>“D”</b> which resets the score to 0. I will go into more of the specifics later but for now this is how it works, and the controls are Basic WASD bindings, though i may go for a HJKL style later. -</p> -</div> -</div> -<div id="outline-container-org37eeebf" class="outline-2"> -<h2 id="org37eeebf">The code :</h2> -<div class="outline-text-2" id="text-org37eeebf"> -<div class="org-src-container"> -<pre class="src src-c"><span class="linenr"> 1: </span><span style="color: #f9e2af;">#include</span> <span style="color: #f38ba8;"><</span><span style="color: #a6e3a1;">stdio.h</span><span style="color: #f38ba8;">></span> -<span class="linenr"> 2: </span><span style="color: #f9e2af;">#include</span> <span style="color: #f38ba8;"><</span><span style="color: #a6e3a1;">stdlib.h</span><span style="color: #f38ba8;">></span> -<span class="linenr"> 3: </span><span style="color: #f9e2af;">int</span> <span style="color: #89b4fa;">main</span><span style="color: #f38ba8;">(</span><span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">argc</span>, <span style="color: #f9e2af;">char</span> *<span style="color: #cdd6f4;">argv</span><span style="color: #fab387;">[]</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr"> 4: </span> <span style="color: #f9e2af;">char</span> <span style="color: #cdd6f4;">input</span>,<span style="color: #cdd6f4;">map</span><span style="color: #fab387;">[</span><span style="color: #fab387;">5</span><span style="color: #fab387;">][</span><span style="color: #fab387;">5</span><span style="color: #fab387;">]</span> = <span style="color: #fab387;">{</span> -<span class="linenr"> 5: </span> <span style="color: #f9e2af;">{</span><span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span><span style="color: #f9e2af;">}</span>, -<span class="linenr"> 6: </span> <span style="color: #f9e2af;">{</span><span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span><span style="color: #f9e2af;">}</span>, -<span class="linenr"> 7: </span> <span style="color: #f9e2af;">{</span><span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span><span style="color: #f9e2af;">}</span>, -<span class="linenr"> 8: </span> <span style="color: #f9e2af;">{</span><span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span><span style="color: #f9e2af;">}</span>, -<span class="linenr"> 9: </span> <span style="color: #f9e2af;">{</span><span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span>, <span style="color: #a6e3a1;">'-'</span><span style="color: #f9e2af;">}</span> -<span class="linenr"> 10: </span> <span style="color: #fab387;">}</span>; -<span class="linenr"> 11: </span> <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">stop</span>=<span style="color: #fab387;">0</span>,<span style="color: #cdd6f4;">i</span>=<span style="color: #fab387;">0</span>,<span style="color: #cdd6f4;">moves</span>=<span style="color: #fab387;">0</span>,<span style="color: #cdd6f4;">score</span>=<span style="color: #fab387;">0</span>,<span style="color: #cdd6f4;">pos</span><span style="color: #fab387;">[</span><span style="color: #fab387;">2</span><span style="color: #fab387;">]</span> = <span style="color: #fab387;">{</span><span style="color: #fab387;">2</span>, <span style="color: #fab387;">2</span><span style="color: #fab387;">}</span>; -<span class="linenr"> 12: </span> <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">bonus</span><span style="color: #fab387;">[</span><span style="color: #fab387;">2</span><span style="color: #fab387;">]</span>; -<span class="linenr"> 13: </span> <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">trap</span><span style="color: #fab387;">[</span><span style="color: #fab387;">2</span><span style="color: #fab387;">]</span> ; -<span class="linenr"> 14: </span> <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">death</span><span style="color: #fab387;">[</span><span style="color: #fab387;">2</span><span style="color: #fab387;">]</span>; -<span class="linenr"> 15: </span> map<span style="color: #fab387;">[</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">][</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">]</span> = <span style="color: #a6e3a1;">'+'</span>; -<span class="linenr"> 16: </span> <span style="color: #cba6f7;">do</span><span style="color: #fab387;">{</span> -<span class="linenr"> 17: </span> bonus<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span> = arc4random_uniform<span style="color: #f9e2af;">(</span><span style="color: #fab387;">5</span><span style="color: #f9e2af;">)</span>; bonus<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span> = arc4random_uniform<span style="color: #f9e2af;">(</span><span style="color: #fab387;">5</span><span style="color: #f9e2af;">)</span>; -<span class="linenr"> 18: </span> trap<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span> = arc4random_uniform<span style="color: #f9e2af;">(</span><span style="color: #fab387;">5</span><span style="color: #f9e2af;">)</span>; trap<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span> = arc4random_uniform<span style="color: #f9e2af;">(</span><span style="color: #fab387;">5</span><span style="color: #f9e2af;">)</span>; -<span class="linenr"> 19: </span> death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span> = arc4random_uniform<span style="color: #f9e2af;">(</span><span style="color: #fab387;">5</span><span style="color: #f9e2af;">)</span>; death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span> = arc4random_uniform<span style="color: #f9e2af;">(</span><span style="color: #fab387;">5</span><span style="color: #f9e2af;">)</span>; -<span class="linenr"> 20: </span> <span style="color: #fab387;">}</span><span style="color: #cba6f7;">while</span><span style="color: #fab387;">(</span><span style="color: #f9e2af;">(</span>bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span><span style="color: #fab387;">)</span>; -<span class="linenr"> 21: </span> map<span style="color: #fab387;">[</span>bonus<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">][</span>bonus<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">]</span> = <span style="color: #a6e3a1;">'B'</span>; -<span class="linenr"> 22: </span> map<span style="color: #fab387;">[</span>trap<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">][</span>trap<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">]</span> = <span style="color: #a6e3a1;">'T'</span>; -<span class="linenr"> 23: </span> map<span style="color: #fab387;">[</span>death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">][</span>death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">]</span> = <span style="color: #a6e3a1;">'D'</span>; -<span class="linenr"> 24: </span> <span style="color: #cba6f7;">do</span><span style="color: #fab387;">{</span> -<span class="linenr"> 25: </span> printf<span style="color: #f9e2af;">(</span><span style="color: #a6e3a1;">"Map:\n"</span><span style="color: #f9e2af;">)</span>; -<span class="linenr"> 26: </span> <span style="color: #cba6f7;">for</span> <span style="color: #f9e2af;">(</span><span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">i</span> = <span style="color: #fab387;">0</span>; i < <span style="color: #fab387;">5</span>; i++<span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 27: </span> <span style="color: #cba6f7;">for</span> <span style="color: #a6e3a1;">(</span><span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">j</span> = <span style="color: #fab387;">0</span>; j < <span style="color: #fab387;">5</span>; j++<span style="color: #a6e3a1;">)</span> <span style="color: #a6e3a1;">{</span> -<span class="linenr"> 28: </span> printf<span style="color: #f38ba8;">(</span><span style="color: #a6e3a1;">"%c "</span>, map<span style="color: #fab387;">[</span>i<span style="color: #fab387;">][</span>j<span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span>; -<span class="linenr"> 29: </span> <span style="color: #a6e3a1;">}</span> -<span class="linenr"> 30: </span> printf<span style="color: #a6e3a1;">(</span><span style="color: #a6e3a1;">"\n"</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr"> 31: </span> <span style="color: #f9e2af;">}</span> -<span class="linenr"> 32: </span> printf<span style="color: #f9e2af;">(</span><span style="color: #a6e3a1;">"Score: %d\n"</span>, score<span style="color: #f9e2af;">)</span>; -<span class="linenr"> 33: </span> printf<span style="color: #f9e2af;">(</span><span style="color: #a6e3a1;">"Moves: %d\n"</span>, moves<span style="color: #f9e2af;">)</span>; -<span class="linenr"> 34: </span> printf<span style="color: #f9e2af;">(</span><span style="color: #a6e3a1;">"Enter a direction (w,a,s,d) or c to quit: "</span><span style="color: #f9e2af;">)</span>; -<span class="linenr"> 35: </span> scanf<span style="color: #f9e2af;">(</span><span style="color: #a6e3a1;">" %c"</span>, &input<span style="color: #f9e2af;">)</span>; -<span class="linenr"> 36: </span><span style="color: #6c7086;">// </span><span style="color: #6c7086;">pos[0] updown pos[1] lr</span> -<span class="linenr"> 37: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>input == <span style="color: #a6e3a1;">'w'</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 38: </span> printf<span style="color: #a6e3a1;">(</span><span style="color: #a6e3a1;">"Moving up\n"</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr"> 39: </span> map<span style="color: #a6e3a1;">[</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">][</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr"> 40: </span> <span style="color: #cba6f7;">if</span> <span style="color: #a6e3a1;">(</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span> == <span style="color: #fab387;">0</span><span style="color: #a6e3a1;">)</span> <span style="color: #a6e3a1;">{</span> -<span class="linenr"> 41: </span> pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span> = <span style="color: #fab387;">4</span>; -<span class="linenr"> 42: </span> <span style="color: #a6e3a1;">}</span> -<span class="linenr"> 43: </span> <span style="color: #cba6f7;">else</span> <span style="color: #a6e3a1;">{</span> -<span class="linenr"> 44: </span> pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span>--; -<span class="linenr"> 45: </span> <span style="color: #a6e3a1;">}</span> -<span class="linenr"> 46: </span> <span style="color: #f9e2af;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>input == <span style="color: #a6e3a1;">'a'</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 47: </span> printf<span style="color: #a6e3a1;">(</span><span style="color: #a6e3a1;">"Moving left\n"</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr"> 48: </span> map<span style="color: #a6e3a1;">[</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">][</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr"> 49: </span> <span style="color: #cba6f7;">if</span> <span style="color: #a6e3a1;">(</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span> == <span style="color: #fab387;">0</span><span style="color: #a6e3a1;">)</span> <span style="color: #a6e3a1;">{</span> -<span class="linenr"> 50: </span> pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span> = <span style="color: #fab387;">4</span>; -<span class="linenr"> 51: </span> <span style="color: #a6e3a1;">}</span> -<span class="linenr"> 52: </span> <span style="color: #cba6f7;">else</span> <span style="color: #a6e3a1;">{</span> -<span class="linenr"> 53: </span> pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span>--; -<span class="linenr"> 54: </span> <span style="color: #a6e3a1;">}</span> -<span class="linenr"> 55: </span> <span style="color: #f9e2af;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>input == <span style="color: #a6e3a1;">'s'</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 56: </span> -<span class="linenr"> 57: </span> printf<span style="color: #a6e3a1;">(</span><span style="color: #a6e3a1;">"Moving down\n"</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr"> 58: </span> map<span style="color: #a6e3a1;">[</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">][</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr"> 59: </span> <span style="color: #cba6f7;">if</span> <span style="color: #a6e3a1;">(</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span> == <span style="color: #fab387;">4</span><span style="color: #a6e3a1;">)</span> <span style="color: #a6e3a1;">{</span> -<span class="linenr"> 60: </span> pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span> = <span style="color: #fab387;">0</span>; -<span class="linenr"> 61: </span> <span style="color: #a6e3a1;">}</span> -<span class="linenr"> 62: </span> <span style="color: #cba6f7;">else</span> <span style="color: #a6e3a1;">{</span> -<span class="linenr"> 63: </span> pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span>++; -<span class="linenr"> 64: </span> <span style="color: #a6e3a1;">}</span> -<span class="linenr"> 65: </span> <span style="color: #f9e2af;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>input == <span style="color: #a6e3a1;">'d'</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 66: </span> printf<span style="color: #a6e3a1;">(</span><span style="color: #a6e3a1;">"Moving right\n"</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr"> 67: </span> map<span style="color: #a6e3a1;">[</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">][</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr"> 68: </span> <span style="color: #cba6f7;">if</span> <span style="color: #a6e3a1;">(</span>pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span> == <span style="color: #fab387;">4</span><span style="color: #a6e3a1;">)</span> <span style="color: #a6e3a1;">{</span> -<span class="linenr"> 69: </span> pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span> = <span style="color: #fab387;">0</span>; -<span class="linenr"> 70: </span> <span style="color: #a6e3a1;">}</span> -<span class="linenr"> 71: </span> <span style="color: #cba6f7;">else</span> <span style="color: #a6e3a1;">{</span> -<span class="linenr"> 72: </span> pos<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span>++; -<span class="linenr"> 73: </span> <span style="color: #a6e3a1;">}</span> -<span class="linenr"> 74: </span> <span style="color: #f9e2af;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>input == <span style="color: #a6e3a1;">'c'</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 75: </span> printf<span style="color: #a6e3a1;">(</span><span style="color: #a6e3a1;">"Quitting\n"</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr"> 76: </span> <span style="color: #f9e2af;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 77: </span> printf<span style="color: #a6e3a1;">(</span><span style="color: #a6e3a1;">"Invalid input\n"</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr"> 78: </span> <span style="color: #f9e2af;">}</span> -<span class="linenr"> 79: </span> map<span style="color: #f9e2af;">[</span>pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">][</span>pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">]</span> = <span style="color: #a6e3a1;">'+'</span>; -<span class="linenr"> 80: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 81: </span> score++; -<span class="linenr"> 82: </span> <span style="color: #cba6f7;">do</span><span style="color: #a6e3a1;">{</span> -<span class="linenr"> 83: </span> bonus<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr"> 84: </span> bonus<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr"> 85: </span> <span style="color: #a6e3a1;">}</span><span style="color: #cba6f7;">while</span><span style="color: #a6e3a1;">(</span><span style="color: #f38ba8;">(</span>bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr"> 86: </span> <span style="color: #f9e2af;">}</span> -<span class="linenr"> 87: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 88: </span> score--; -<span class="linenr"> 89: </span> <span style="color: #cba6f7;">do</span><span style="color: #a6e3a1;">{</span> -<span class="linenr"> 90: </span> trap<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr"> 91: </span> trap<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr"> 92: </span> <span style="color: #a6e3a1;">}</span><span style="color: #cba6f7;">while</span><span style="color: #a6e3a1;">(</span><span style="color: #f38ba8;">(</span>trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr"> 93: </span> <span style="color: #f9e2af;">}</span> -<span class="linenr"> 94: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr"> 95: </span> score = <span style="color: #fab387;">0</span>; -<span class="linenr"> 96: </span> <span style="color: #cba6f7;">do</span><span style="color: #a6e3a1;">{</span> -<span class="linenr"> 97: </span> death<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr"> 98: </span> death<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr"> 99: </span> <span style="color: #a6e3a1;">}</span><span style="color: #cba6f7;">while</span><span style="color: #a6e3a1;">(</span><span style="color: #f38ba8;">(</span>death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr">100: </span> <span style="color: #f9e2af;">}</span> -<span class="linenr">101: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>score % <span style="color: #fab387;">3</span> == <span style="color: #fab387;">0</span> && score != <span style="color: #fab387;">0</span> && stop == <span style="color: #fab387;">0</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr">102: </span> map<span style="color: #a6e3a1;">[</span>death<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">][</span>death<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span><span style="color: #a6e3a1;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr">103: </span> <span style="color: #cba6f7;">do</span><span style="color: #a6e3a1;">{</span> -<span class="linenr">104: </span> death<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr">105: </span> death<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr">106: </span> <span style="color: #a6e3a1;">}</span><span style="color: #cba6f7;">while</span><span style="color: #a6e3a1;">(</span><span style="color: #f38ba8;">(</span>death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr">107: </span> stop = <span style="color: #fab387;">1</span>; -<span class="linenr">108: </span> <span style="color: #f9e2af;">}</span> -<span class="linenr">109: </span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>score % <span style="color: #fab387;">3</span> != <span style="color: #fab387;">0</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr">110: </span> stop = <span style="color: #fab387;">0</span>; -<span class="linenr">111: </span> <span style="color: #f9e2af;">}</span> -<span class="linenr">112: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f9e2af;">(</span>moves % <span style="color: #fab387;">5</span> == <span style="color: #fab387;">0</span> && moves != <span style="color: #fab387;">0</span><span style="color: #f9e2af;">)</span> <span style="color: #f9e2af;">{</span> -<span class="linenr">113: </span> <span style="color: #cba6f7;">do</span><span style="color: #a6e3a1;">{</span> -<span class="linenr">114: </span> map<span style="color: #f38ba8;">[</span>trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">][</span>trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr">115: </span> trap<span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr">116: </span> trap<span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span>= arc4random_uniform<span style="color: #f38ba8;">(</span><span style="color: #fab387;">5</span><span style="color: #f38ba8;">)</span>; -<span class="linenr">117: </span> <span style="color: #a6e3a1;">}</span><span style="color: #cba6f7;">while</span><span style="color: #a6e3a1;">(</span><span style="color: #f38ba8;">(</span>trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> || <span style="color: #f38ba8;">(</span>trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == pos<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span><span style="color: #a6e3a1;">)</span>; -<span class="linenr">118: </span> -<span class="linenr">119: </span> <span style="color: #f9e2af;">}</span> -<span class="linenr">120: </span> map<span style="color: #f9e2af;">[</span>bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">][</span>bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">]</span> = <span style="color: #a6e3a1;">'B'</span>; -<span class="linenr">121: </span> map<span style="color: #f9e2af;">[</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">][</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">]</span> = <span style="color: #a6e3a1;">'T'</span>; -<span class="linenr">122: </span> map<span style="color: #f9e2af;">[</span>death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">][</span>death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">]</span> = <span style="color: #a6e3a1;">'D'</span>; -<span class="linenr">123: </span> moves++; -<span class="linenr">124: </span> <span style="color: #fab387;">}</span><span style="color: #cba6f7;">while</span><span style="color: #fab387;">(</span>input != <span style="color: #a6e3a1;">'c'</span><span style="color: #fab387;">)</span>; -<span class="linenr">125: </span> <span style="color: #cba6f7;">return</span> <span style="color: #fab387;">0</span>; -<span class="linenr">126: </span><span style="color: #f38ba8;">}</span> -<span class="linenr">127: </span> -</pre> -</div> - - -<p> -Let’s go step by step and see what we can fix or improve, to start off, line 4 to 10 can be reduced to 7 or 8 lines (which will be beneficial later too) -</p> -<div class="org-src-container"> -<pre class="src src-c"><span class="linenr"> 4: </span><span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">n</span>=<span style="color: #fab387;">5</span>,<span style="color: #cdd6f4;">m</span>=<span style="color: #fab387;">5</span>; -<span class="linenr"> 5: </span><span style="color: #f9e2af;">char</span> <span style="color: #cdd6f4;">input</span>,<span style="color: #cdd6f4;">map</span><span style="color: #f38ba8;">[</span><span style="color: #fab387;">50</span><span style="color: #f38ba8;">][</span><span style="color: #fab387;">50</span><span style="color: #f38ba8;">]</span>; -<span class="linenr"> 6: </span> <span style="color: #cba6f7;">for</span> <span style="color: #f38ba8;">(</span><span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">i</span> = <span style="color: #fab387;">0</span>; i < n; i++<span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr"> 7: </span> <span style="color: #cba6f7;">for</span> <span style="color: #fab387;">(</span><span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">j</span> = <span style="color: #fab387;">0</span>; j < m; j++<span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> -<span class="linenr"> 8: </span> map<span style="color: #f9e2af;">[</span>i<span style="color: #f9e2af;">][</span>j<span style="color: #f9e2af;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr"> 9: </span> <span style="color: #fab387;">}</span> -<span class="linenr">10: </span> <span style="color: #f38ba8;">}</span> -<span class="linenr">11: </span> -</pre> -</div> - -<p> -For now at least, n and m are hardcoded to 5, but this will change later. And I picked 50x50 as a max size because why not -</p> - -<p> -Of course we have the usual inits on line 11, though since we are using variables instead of hardcoding 5, we will have to find the center by ourselves -</p> -<div class="org-src-container"> -<pre class="src src-c"><span class="linenr">11: </span> <span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">stop</span>=<span style="color: #fab387;">0</span>,<span style="color: #cdd6f4;">i</span>=<span style="color: #fab387;">0</span>,<span style="color: #cdd6f4;">moves</span>=<span style="color: #fab387;">0</span>,<span style="color: #cdd6f4;">score</span>=<span style="color: #fab387;">0</span>,<span style="color: #cdd6f4;">pos</span><span style="color: #f38ba8;">[</span><span style="color: #fab387;">2</span><span style="color: #f38ba8;">]</span> = <span style="color: #f38ba8;">{</span>n/<span style="color: #fab387;">2</span>,m/<span style="color: #fab387;">2</span><span style="color: #f38ba8;">}</span>; -</pre> -</div> - -<p> -This is getting better, of course we then initialize the coordinates of bonus, trap, and death, and set the player as a <b>’+’</b> in the field. -</p> - - -<p> -Here comes the line 17-21, where it generates a random coordinate for the aforementioned pickups, and do that until there is no conflict between eachother and the player) here we will need to change it a tiny bit. -</p> -<div class="org-src-container"> -<pre class="src src-c"><span class="linenr">17: </span> <span style="color: #f9e2af;">bonus</span><span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span> = arc4random_uniform<span style="color: #f38ba8;">(</span>n<span style="color: #f38ba8;">)</span>; <span style="color: #f9e2af;">bonus</span><span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span> = arc4random_uniform<span style="color: #f38ba8;">(</span>m<span style="color: #f38ba8;">)</span>; -<span class="linenr">18: </span> <span style="color: #f9e2af;">trap</span><span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span> = arc4random_uniform<span style="color: #f38ba8;">(</span>n<span style="color: #f38ba8;">)</span>; <span style="color: #f9e2af;">trap</span><span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span> = arc4random_uniform<span style="color: #f38ba8;">(</span>m<span style="color: #f38ba8;">)</span>; -<span class="linenr">19: </span> <span style="color: #f9e2af;">death</span><span style="color: #f38ba8;">[</span><span style="color: #fab387;">0</span><span style="color: #f38ba8;">]</span> = arc4random_uniform<span style="color: #f38ba8;">(</span>n<span style="color: #f38ba8;">)</span>; <span style="color: #f9e2af;">death</span><span style="color: #f38ba8;">[</span><span style="color: #fab387;">1</span><span style="color: #f38ba8;">]</span> = arc4random_uniform<span style="color: #f38ba8;">(</span>m<span style="color: #f38ba8;">)</span>; -</pre> -</div> - -<p> -Looking good so far!!, We then have line 21-23 which also shows the pickups as their respective symbols in the map. -</p> - - -<p> -The main interactive program starts here, which will learn at least one time and stop if the received input is a <b>’c’</b>, it starts with a nested for loop on line 26 up to 31 to show the content of the map, nothing fancy, just some matrix stuff. we need to change the 5 though! -</p> -<div class="org-src-container"> -<pre class="src src-c"><span class="linenr">26: </span> <span style="color: #cba6f7;">for</span> <span style="color: #f38ba8;">(</span><span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">i</span> = <span style="color: #fab387;">0</span>; i < n; i++<span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">27: </span> <span style="color: #cba6f7;">for</span> <span style="color: #fab387;">(</span><span style="color: #f9e2af;">int</span> <span style="color: #cdd6f4;">j</span> = <span style="color: #fab387;">0</span>; j < m; j++<span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> -<span class="linenr">28: </span> printf<span style="color: #f9e2af;">(</span><span style="color: #a6e3a1;">"%c "</span>, map<span style="color: #a6e3a1;">[</span>i<span style="color: #a6e3a1;">][</span>j<span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span>; -<span class="linenr">29: </span> <span style="color: #fab387;">}</span> -<span class="linenr">30: </span> printf<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"\n"</span><span style="color: #fab387;">)</span>; -<span class="linenr">31: </span> <span style="color: #f38ba8;">}</span> -<span class="linenr">32: </span> -</pre> -</div> -<p> -We show the score and the moves too, which at the start of the game are set to 0. and we prompt the user for a direction. Note here the space before the %c, this basically allows for the program to not choke on newlines and also even if the user writes multiple keys at the same time, they will still be done, like <b>ww</b> will make the player move twice up. -</p> - -<p> -After that we have some logic which should also be changed to account for the n and m changes yet again -</p> -<div class="org-src-container"> -<pre class="src src-c"><span class="linenr">37: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>input == <span style="color: #a6e3a1;">'w'</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">38: </span> printf<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Moving up\n"</span><span style="color: #fab387;">)</span>; -<span class="linenr">39: </span> map<span style="color: #fab387;">[</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">][</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr">40: </span> <span style="color: #cba6f7;">if</span> <span style="color: #fab387;">(</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span> == <span style="color: #fab387;">0</span><span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> -<span class="linenr">41: </span> pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span> = n-<span style="color: #fab387;">1</span>; -<span class="linenr">42: </span> <span style="color: #fab387;">}</span> -<span class="linenr">43: </span> <span style="color: #cba6f7;">else</span> <span style="color: #fab387;">{</span> -<span class="linenr">44: </span> pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span>--; -<span class="linenr">45: </span> <span style="color: #fab387;">}</span> -<span class="linenr">46: </span> <span style="color: #f38ba8;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>input == <span style="color: #a6e3a1;">'a'</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">47: </span> printf<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Moving left\n"</span><span style="color: #fab387;">)</span>; -<span class="linenr">48: </span> map<span style="color: #fab387;">[</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">][</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr">49: </span> <span style="color: #cba6f7;">if</span> <span style="color: #fab387;">(</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span> == <span style="color: #fab387;">0</span><span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> -<span class="linenr">50: </span> pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span> = m-<span style="color: #fab387;">1</span>; -<span class="linenr">51: </span> <span style="color: #fab387;">}</span> -<span class="linenr">52: </span> <span style="color: #cba6f7;">else</span> <span style="color: #fab387;">{</span> -<span class="linenr">53: </span> pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span>--; -<span class="linenr">54: </span> <span style="color: #fab387;">}</span> -<span class="linenr">55: </span> <span style="color: #f38ba8;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>input == <span style="color: #a6e3a1;">'s'</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">56: </span> -<span class="linenr">57: </span> printf<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Moving down\n"</span><span style="color: #fab387;">)</span>; -<span class="linenr">58: </span> map<span style="color: #fab387;">[</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">][</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr">59: </span> <span style="color: #cba6f7;">if</span> <span style="color: #fab387;">(</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span> == n-<span style="color: #fab387;">1</span><span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> -<span class="linenr">60: </span> pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span> = <span style="color: #fab387;">0</span>; -<span class="linenr">61: </span> <span style="color: #fab387;">}</span> -<span class="linenr">62: </span> <span style="color: #cba6f7;">else</span> <span style="color: #fab387;">{</span> -<span class="linenr">63: </span> pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span>++; -<span class="linenr">64: </span> <span style="color: #fab387;">}</span> -<span class="linenr">65: </span> <span style="color: #f38ba8;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>input == <span style="color: #a6e3a1;">'d'</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">66: </span> printf<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Moving right\n"</span><span style="color: #fab387;">)</span>; -<span class="linenr">67: </span> map<span style="color: #fab387;">[</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">][</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr">68: </span> <span style="color: #cba6f7;">if</span> <span style="color: #fab387;">(</span>pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span> == m-<span style="color: #fab387;">1</span><span style="color: #fab387;">)</span> <span style="color: #fab387;">{</span> -<span class="linenr">69: </span> pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span> = <span style="color: #fab387;">0</span>; -<span class="linenr">70: </span> <span style="color: #fab387;">}</span> -<span class="linenr">71: </span> <span style="color: #cba6f7;">else</span> <span style="color: #fab387;">{</span> -<span class="linenr">72: </span> pos<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span>++; -<span class="linenr">73: </span> <span style="color: #fab387;">}</span> -<span class="linenr">74: </span> <span style="color: #f38ba8;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>input == <span style="color: #a6e3a1;">'c'</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">75: </span> printf<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Quitting\n"</span><span style="color: #fab387;">)</span>; -<span class="linenr">76: </span> <span style="color: #f38ba8;">}</span> <span style="color: #cba6f7;">else</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">77: </span> printf<span style="color: #fab387;">(</span><span style="color: #a6e3a1;">"Invalid input\n"</span><span style="color: #fab387;">)</span>; -<span class="linenr">78: </span> <span style="color: #f38ba8;">}</span> -</pre> -</div> - -<p> -What this achieves is the “teleportation effect” whenever you are at the border of the screen! -</p> - - -<p> -Now we fix things from line 80 to the end of the program, aka replacing ever occurrence of 5 with n or m -</p> -<div class="org-src-container"> -<pre class="src src-c"><span class="linenr"> 80: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>pos<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && pos<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == bonus<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr"> 81: </span> score++; -<span class="linenr"> 82: </span> <span style="color: #cba6f7;">do</span><span style="color: #fab387;">{</span> -<span class="linenr"> 83: </span> bonus<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>n<span style="color: #f9e2af;">)</span>; -<span class="linenr"> 84: </span> bonus<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>m<span style="color: #f9e2af;">)</span>; -<span class="linenr"> 85: </span> <span style="color: #fab387;">}</span><span style="color: #cba6f7;">while</span><span style="color: #fab387;">(</span><span style="color: #f9e2af;">(</span>bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span><span style="color: #fab387;">)</span>; -<span class="linenr"> 86: </span> <span style="color: #f38ba8;">}</span> -<span class="linenr"> 87: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>pos<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == trap<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && pos<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == trap<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr"> 88: </span> score--; -<span class="linenr"> 89: </span> <span style="color: #cba6f7;">do</span><span style="color: #fab387;">{</span> -<span class="linenr"> 90: </span> trap<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>n<span style="color: #f9e2af;">)</span>; -<span class="linenr"> 91: </span> trap<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>m<span style="color: #f9e2af;">)</span>; -<span class="linenr"> 92: </span> <span style="color: #fab387;">}</span><span style="color: #cba6f7;">while</span><span style="color: #fab387;">(</span><span style="color: #f9e2af;">(</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span><span style="color: #fab387;">)</span>; -<span class="linenr"> 93: </span> <span style="color: #f38ba8;">}</span> -<span class="linenr"> 94: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>pos<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> == death<span style="color: #fab387;">[</span><span style="color: #fab387;">0</span><span style="color: #fab387;">]</span> && pos<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span> == death<span style="color: #fab387;">[</span><span style="color: #fab387;">1</span><span style="color: #fab387;">]</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr"> 95: </span> score = <span style="color: #fab387;">0</span>; -<span class="linenr"> 96: </span> <span style="color: #cba6f7;">do</span><span style="color: #fab387;">{</span> -<span class="linenr"> 97: </span> death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>n<span style="color: #f9e2af;">)</span>; -<span class="linenr"> 98: </span> death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>m<span style="color: #f9e2af;">)</span>; -<span class="linenr"> 99: </span> <span style="color: #fab387;">}</span><span style="color: #cba6f7;">while</span><span style="color: #fab387;">(</span><span style="color: #f9e2af;">(</span>death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span><span style="color: #fab387;">)</span>; -<span class="linenr">100: </span> <span style="color: #f38ba8;">}</span> -<span class="linenr">101: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>score % <span style="color: #fab387;">3</span> == <span style="color: #fab387;">0</span> && score != <span style="color: #fab387;">0</span> && stop == <span style="color: #fab387;">0</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">102: </span> map<span style="color: #fab387;">[</span>death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">][</span>death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span><span style="color: #fab387;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr">103: </span> <span style="color: #cba6f7;">do</span><span style="color: #fab387;">{</span> -<span class="linenr">104: </span> death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>n<span style="color: #f9e2af;">)</span>; -<span class="linenr">105: </span> death<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>m<span style="color: #f9e2af;">)</span>; -<span class="linenr">106: </span> <span style="color: #fab387;">}</span><span style="color: #cba6f7;">while</span><span style="color: #fab387;">(</span><span style="color: #f9e2af;">(</span>death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span><span style="color: #fab387;">)</span>; -<span class="linenr">107: </span> stop = <span style="color: #fab387;">1</span>; -<span class="linenr">108: </span> <span style="color: #f38ba8;">}</span> -<span class="linenr">109: </span> <span style="color: #cba6f7;">else</span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>score % <span style="color: #fab387;">3</span> != <span style="color: #fab387;">0</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">110: </span> stop = <span style="color: #fab387;">0</span>; -<span class="linenr">111: </span> <span style="color: #f38ba8;">}</span> -<span class="linenr">112: </span> <span style="color: #cba6f7;">if</span> <span style="color: #f38ba8;">(</span>moves % <span style="color: #fab387;">5</span> == <span style="color: #fab387;">0</span> && moves != <span style="color: #fab387;">0</span><span style="color: #f38ba8;">)</span> <span style="color: #f38ba8;">{</span> -<span class="linenr">113: </span> <span style="color: #cba6f7;">do</span><span style="color: #fab387;">{</span> -<span class="linenr">114: </span> map<span style="color: #f9e2af;">[</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">][</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">]</span> = <span style="color: #a6e3a1;">'-'</span>; -<span class="linenr">115: </span> trap<span style="color: #f9e2af;">[</span><span style="color: #fab387;">0</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>n<span style="color: #f9e2af;">)</span>; -<span class="linenr">116: </span> trap<span style="color: #f9e2af;">[</span><span style="color: #fab387;">1</span><span style="color: #f9e2af;">]</span>= arc4random_uniform<span style="color: #f9e2af;">(</span>m<span style="color: #f9e2af;">)</span>; -<span class="linenr">117: </span> <span style="color: #fab387;">}</span><span style="color: #cba6f7;">while</span><span style="color: #fab387;">(</span><span style="color: #f9e2af;">(</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == bonus<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == death<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span> || <span style="color: #f9e2af;">(</span>trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">0</span><span style="color: #a6e3a1;">]</span> && trap<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span> == pos<span style="color: #a6e3a1;">[</span><span style="color: #fab387;">1</span><span style="color: #a6e3a1;">]</span><span style="color: #f9e2af;">)</span><span style="color: #fab387;">)</span>; -<span class="linenr">118: </span> -<span class="linenr">119: </span> <span style="color: #f38ba8;">}</span> -</pre> -</div> - - -<p> -Aaaaand this should be it -</p> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2024-02-22 Thu 19:09</p> -</div> -</body> -</html> diff --git a/blog/lisp/episode1.html b/blog/lisp/episode1.html deleted file mode 100644 index 72c5b97..0000000 --- a/blog/lisp/episode1.html +++ /dev/null @@ -1,29 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2023-12-17 Sun 19:04 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>Learn Lisp With me. Episode 1</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../../../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../../../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="https://crystal.tilde.institute/favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href="../index.html"> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title">Learn Lisp With me. Episode 1</h1> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2023-12-17 Sun 19:04</p> -</div> -</body> -</html> diff --git a/blog/misc/merlin.html b/blog/misc/merlin.html deleted file mode 100644 index ec7f975..0000000 --- a/blog/misc/merlin.html +++ /dev/null @@ -1,191 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2024-04-12 Fri 19:51 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>ON MERLIN'S BEARD</title> -<meta name="author" content="Crystal for my sloth" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="../../../favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href=""> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title">ON MERLIN’S BEARD</h1> -<p> -Let’s say, hypothetically, you have a <b>Xiaomi Redmi Note 9</b> (codenamed <b>Merlin</b>), and we would assume that it’s broken in a way that it shows the <b>Xiaomi logo</b> only then reboots/shuts-down, your first solution would be “Oh let’s take it to a repairshop, they would fix it” but why do so when you could fix it at home, alone, with the help of this little guide. -</p> -<div id="outline-container-org88c83c3" class="outline-2"> -<h2 id="org88c83c3">Axioms :</h2> -<div class="outline-text-2" id="text-org88c83c3"> -<p> -We will assume the following things : -</p> -<ul class="org-ul"> -<li>You have a Redmi Note 9…or any Redmi, but some steps WILL vary ever so slightly.</li> -<li>The phone at least gives a sign of life, the Xiaomi logo is well enough.</li> -<li>You have a PC, preferably running the second best OS known to mankind, <b>Linux !!!</b>. If you are not running Linux, a good start is <b>Ubuntu</b> (we will assume the usage of a <b>Debian</b>-based distro here, if you use anything other than them, you are probably smart enough to figure this shit yourself)</li> -<li>You have a good USB-C cable.</li> -<li>You have a working brain.</li> -</ul> -</div> -</div> -<div id="outline-container-org0e634c8" class="outline-2"> -<h2 id="org0e634c8">Step Uno : Downloading the required files and the medkits :</h2> -<div class="outline-text-2" id="text-org0e634c8"> -</div> -<div id="outline-container-orgdbc8e67" class="outline-3"> -<h3 id="orgdbc8e67">android-tools :</h3> -<div class="outline-text-3" id="text-orgdbc8e67"> -<div class="org-src-container"> -<pre class="src src-sh"><span style="color: #f9e2af;">sudo</span> apt update -<span style="color: #f9e2af;">sudo</span> apt install android-tools-adb android-tools-fastboot -</pre> -</div> -</div> -</div> -<div id="outline-container-orga65ea6a" class="outline-3"> -<h3 id="orga65ea6a">mtkclient and it’s dependencies :</h3> -<div class="outline-text-3" id="text-orga65ea6a"> -</div> -<div id="outline-container-orgcbafb81" class="outline-4"> -<h4 id="orgcbafb81">Dependencies :</h4> -<div class="outline-text-4" id="text-orgcbafb81"> -<div class="org-src-container"> -<pre class="src src-sh"><span style="color: #f9e2af;">sudo</span> apt install python3 <span style="color: #f9e2af;">git</span> libusb-1.0-0 python3-pip -</pre> -</div> -</div> -</div> -<div id="outline-container-org4a33127" class="outline-4"> -<h4 id="org4a33127">Grab the files :</h4> -<div class="outline-text-4" id="text-org4a33127"> -<div class="org-src-container"> -<pre class="src src-shell"><span style="color: #f9e2af;">git</span> clone https://github.com/bkerler/mtkclient -<span style="color: #f9e2af;">cd</span> mtkclient -pip3 install . -</pre> -</div> -</div> -</div> -<div id="outline-container-orge0a0f85" class="outline-4"> -<h4 id="orge0a0f85">Install rules :</h4> -<div class="outline-text-4" id="text-orge0a0f85"> -<div class="org-src-container"> -<pre class="src src-shell"><span style="color: #f9e2af;">sudo</span> usermod -a -G plugdev $<span style="color: #cdd6f4;">USER</span> -<span style="color: #f9e2af;">sudo</span> usermod -a -G dialout $<span style="color: #cdd6f4;">USER</span> -<span style="color: #f9e2af;">sudo</span> <span style="color: #f9e2af;">cp</span> mtkclient/Setup/Linux/*.rules /etc/udev/rules.d -<span style="color: #f9e2af;">sudo</span> udevadm control -R -</pre> -</div> -<p> -and do <b>NOT</b> forget to reboot, otherwise you will face errors. -</p> -</div> -</div> -</div> -<div id="outline-container-org283a105" class="outline-3"> -<h3 id="org283a105">Fastboot image :</h3> -<div class="outline-text-3" id="text-org283a105"> -<p> -Personally, I prefer to use a custom ROM for these XIMI phones, but since this is a fool-proof guide, we will use the latest <b>Global</b> fastboot image, note that the difference between <b>Global</b> , <b>EEA (European Economic Area)</b> , <b>Turkish</b> , <b>Russian</b> and <b>Taiwan</b> ROMS are little though the Global version is most of the time behind the other ones in terms of updates , but the biggest one comes with the <b>Chinese</b> one, it’s more polished, runs faster, but is filled with Chinese-only apps, and does not have Google services (which is a huge W for me). But at the end of the day, it’s up to you! -</p> - -<p> -We will be using this one <a href="https://xiaomifirmwareupdater.com/miui/merlin/stable/V13.0.2.0.SJOMIXM/">https://xiaomifirmwareupdater.com/miui/merlin/stable/V13.0.2.0.SJOMIXM/</a> which is the Global version of miui. Make sure to scroll all the way <b>Down</b> and download the one with <b>Type: Fastboot</b>, it will be larger in size, but it’s the one we need. Use any mirror that you want, and wait patiently for it to download. Once it finishes, extract it to a folder, it’s a big archive so it will take time. -</p> -</div> -</div> -<div id="outline-container-org4addd56" class="outline-3"> -<h3 id="org4addd56">Meanwhile, mtkclient :</h3> -<div class="outline-text-3" id="text-org4addd56"> -<p> -While waiting for your download to finish, go to your mtkclient folder and run this command: -</p> -<div class="org-src-container"> -<pre class="src src-shell">python mtk_gui -</pre> -</div> -<p> -this should bring up the GUI client, if it doesn’t, replace <b>python</b> with <b>python3</b>. Once it’s running, make sure your phone is powered-off, and plug the USB-C cable into your PC <b>While holding both the Up and Down volume buttons</b> until you see a change in the GUI app. If you notice a red error message on the console which will be running in the background, relaunch using <b>sudo</b>. -</p> - -<p> -Now explore the app but do <b>NOT</b> touch anything with the word <b>Write</b> or <b>Erase</b>, also the ones with <b>Read</b> are useless for you, what is important is looking for the <b>Unlock bootloader</b> button, click on it, and wait until it’s okay, then remove your phone from the cable. aaaand we shoould be done for this part. -</p> -</div> -</div> -<div id="outline-container-org25169bd" class="outline-3"> -<h3 id="org25169bd">The Fun Part :</h3> -<div class="outline-text-3" id="text-org25169bd"> -<p> -Once the fastboot image is downloaded and extracted, go to the folder and look for this file <b>flash_all_except_storage.sh</b> this will be the one you would need. -</p> - -<p> -<b>DO NOT EVER EVER EVER, UNDER ANY CASE, TOUCH A FILE THAT HAS THE WORD LOCK IN IT.</b> -</p> - -<p> -Once you located this file, open a terminal there, and give it exec permissions. Or in other words : -</p> -<div class="org-src-container"> -<pre class="src src-shell"><span style="color: #f9e2af;">chmod</span> +x ./flash_all_except_storage.sh -</pre> -</div> -<p> -and now take your phone <b>again</b> and now Power it on while holding the <b>Vol DOWN</b> button, keep that position until you see a <b>fastboot</b> screen, or a Russian robot rewiring the organs of it’s victim. -</p> - -<p> -Once you see it, plug the phone to the pc, and run -</p> -<div class="org-src-container"> -<pre class="src src-shell"><span style="color: #f9e2af;">sudo</span> fastboot devices -</pre> -</div> -<p> -sudo might not be needed for you, but i dont know why, it never worked for me without sudo (probably the rules step) -</p> - -<p> -Once you see your device in there, it means it recognized it, go again to the folder with <b>flash_all_except_storage</b> and run it -</p> -<div class="org-src-container"> -<pre class="src src-shell"><span style="color: #f9e2af;">sudo</span> ./flash_all_except_storage.sh -</pre> -</div> -</div> -</div> -<div id="outline-container-org95f8d76" class="outline-3"> -<h3 id="org95f8d76">Waiting :</h3> -<div class="outline-text-3" id="text-org95f8d76"> -<p> -This step takes a lot of time, so be sure to let your pc in a place where you don’t risk accidentally moving your phone and disconnecting it. DO NOT CLOSE THE TERMINAL, once it’s finished, it should reboot automatically and voila !! good as knew, and you might even keep your local files if you provide your password -</p> -</div> -</div> -</div> -<div id="outline-container-org1a283a8" class="outline-2"> -<h2 id="org1a283a8">Edge cases :</h2> -<div class="outline-text-2" id="text-org1a283a8"> -<ul class="org-ul"> -<li>If the initial setup (after the reboot) doesn’t work, try the flash_all.sh file instead.</li> -</ul> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal for my sloth</p> -<p class="date">Created: 2024-04-12 Fri 19:51</p> -</div> -</body> -</html> diff --git a/index.html b/index.html deleted file mode 100755 index cb45c72..0000000 --- a/index.html +++ /dev/null @@ -1,209 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2024-04-15 Mon 19:35 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>Crystal's Website 💜</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="favicon.png"> -</head> -<body> -<div id="content" class="content"> -<h1 class="title">Crystal’s Website 💜</h1> -<div id="outline-container-org8f7a256" class="outline-2"> -<h2 id="org8f7a256">Welcome to the wired</h2> -<div class="outline-text-2" id="text-org8f7a256"> -<p> -Hi there, <a href="./super_secret.html">adorable you!</a> -</p> - -<p> -And welcome to my little corner of the internet, here I will be posting my random thoughts, some class notes, random articles, funny links…etc. Basically a way for me to play around with HTML and CSS. -</p> - - -<p> -<b>Note: This web page is designed to be viewed even without JavaScript, the only place where I use JS is in the webring page (If I use them elsewhere, I will put a warning)</b> -</p> - - - -<div id="orgce1fc24" class="figure"> -<p><img src="./src/gifs/Lain_chibi.png" alt="Lain_chibi.png" width="200px" /> -</p> -</div> -</div> -</div> -<div id="outline-container-org25511bb" class="outline-2"> -<h2 id="org25511bb">Articles ( NEW !!!! )</h2> -<div class="outline-text-2" id="text-org25511bb"> -<ul class="org-ul"> -<li><b><a href="./articles/feminism1_alex.html">Existing as a woman is a rebellion</a></b> <i>Thu Nov 2 23:01:23 2023</i></li> -<li><b><a href="./articles/discord.html">Discord : an internet cancer</a></b> <i>Sun Sep 10 15:25:22 2023</i></li> -</ul> -</div> -</div> -<div id="outline-container-orgd53b38a" class="outline-2"> -<h2 id="orgd53b38a">Blogs ( NEWER !!!! )</h2> -<div class="outline-text-2" id="text-orgd53b38a"> -</div> -<div id="outline-container-org2f5194a" class="outline-3"> -<h3 id="org2f5194a">C programming :</h3> -<div class="outline-text-3" id="text-org2f5194a"> -<ul class="org-ul"> -<li><b><a href="./blog/c/cherry.html">Reviving Caesar with a Cherry-flavored Crystal</a></b> <i>Sat Mar 16 21:43:48 2024</i></li> -<li><b><a href="./blog/c/game.html">The Loneliness game</a></b> <i>Wed Feb 14 23:46:35 2024</i></li> -</ul> -</div> -</div> -<div id="outline-container-orge2510ca" class="outline-3"> -<h3 id="orge2510ca">x86 ASM Programming:</h3> -<div class="outline-text-3" id="text-orge2510ca"> -<ul class="org-ul"> -<li><b><a href="./blog/asm/1.html">x86 Assembly from my understanding</a></b></li> -</ul> -</div> -</div> -</div> -<div id="outline-container-orgd024c4a" class="outline-2"> -<h2 id="orgd024c4a">root@localhost $ whoami</h2> -<div class="outline-text-2" id="text-orgd024c4a"> -</div> -<div id="outline-container-orgad0f931" class="outline-3"> -<h3 id="orgad0f931">About me :</h3> -<div class="outline-text-3" id="text-orgad0f931"> -<ul class="org-ul"> -<li>Name : <b>Crystal</b></li> -<li>Age : <b>18 years old</b></li> -<li>Nationality : <b>Algerian</b></li> -<li>Pronouns : <b>*(Any)</b></li> -<li>Sexuality : <b>Aro/Ace cis</b></li> -<li>Political affiliation : <b>Anarchism</b></li> -<li>Hobbies : <b>Include but not limited to programming, exploring new OSes, new music genres and making friends</b></li> -</ul> -<p> -This might surprise you, but I also listen to music (A shocker, right?) though I mostly listen to <b>vaporwave</b> <b>glitchore</b> <b>weirdcore</b> <b>synthwave</b> and <b>dreamcore</b> -</p> - -<p> -If you want to contact me (which would be really surprising) contact me via <a href="mailto:crystaltrd@cumallover.me">mailto:crystaltrd@cumallover.me</a> -</p> -</div> -</div> -<div id="outline-container-orgbbc0da3" class="outline-3"> -<h3 id="orgbbc0da3">About my Navi :</h3> -<div class="outline-text-3" id="text-orgbbc0da3"> -<p> -My current setup is : -</p> -<ul class="org-ul"> -<li>Primary OS: <b>OpenBSD -current</b></li> -<li>Text Editor: <b>Doom Emacs</b></li> -<li>Web Browser: <b>Ungoogled-chromium</b></li> -<li>Desktop Environment: <b>NsCDE</b></li> -<li>Shell: <b>Historic Ksh93</b></li> -<li>Secondary OS: <b>Void Linux</b></li> -<li>Games I play: <b>Hollow Knight</b>, <b>Cult of the lamb</b>, <b>Dead Cells</b> & Rythm games(like <b>Phigros</b> and <b>A dance of fire and ice</b>)</li> -</ul> -<p> -I also host this website on the <a href="https://tilde.institute">https://tilde.institute</a> <b>pubNIX</b> which also runs <b>OpenBSD</b> -</p> - - -<p> -<a href="https://git.tilde.institute/crystal/www">This website is fully open-source with no licensing restrictions, check the source code and feel free to reuse everything!!!</a> -</p> -</div> -</div> -</div> -<div id="outline-container-org62f9f18" class="outline-2"> -<h2 id="org62f9f18">Sign my Guestbook (External website warning)</h2> -<div class="outline-text-2" id="text-org62f9f18"> -<p> -Want to leave a message, opinion, review or a salty insult ? Be sure to Sign my Guestbook then, it takes two seconds but it will mean the world to me !!! -</p> - - -<div id="orga6f5b1c" class="figure"> -<p><a href="https://crystaltilde.123guestbook.com/"><img src="./src/gifs/links/sign_my_guestbook-anim.gif" alt="sign_my_guestbook-anim.gif" /></a> -</p> -</div> -</div> -</div> -<div id="outline-container-org377b58a" class="outline-2"> -<h2 id="org377b58a">Blinkies</h2> -<div class="outline-text-2" id="text-org377b58a"> -<a href="http://validator.w3.org/check?uri=referer"><img - src="./src/gifs/blinkies/valid-xhtml10.png" alt="Valid XHTML 1.0 Strict" height="31" width="88" /></a> - <a href="https://jigsaw.w3.org/css-validator/check/referer"> - <img style="border:0;width:88px;height:31px" - src="./src/gifs/blinkies/vcss.gif" - alt="Valid CSS!" /> -</a> -<p> -<a href="https://nishi.boats/"><img src="./src/gifs/blinkies/nishiboats.jpg" alt="nishiboats.jpg" /></a> <img src="./src/gifs/blinkies/girlsnow.png" alt="girlsnow.png" /> <img src="./src/gifs/blinkies/cookiefree.gif" alt="cookiefree.gif" /> <img src="./src/gifs/blinkies/transnow2.gif" alt="transnow2.gif" /> <img src="./src/gifs/blinkies/gaywebring.gif" alt="gaywebring.gif" /> <img src="./src/gifs/blinkies/tranarchy.gif" alt="tranarchy.gif" /> <img src="./src/gifs/blinkies/button-torrents.gif" alt="button-torrents.gif" /> <img src="./src/gifs/blinkies/tyg.gif" alt="tyg.gif" /> <img src="./src/gifs/blinkies/fuck-google.gif" alt="fuck-google.gif" /> <img src="./src/gifs/blinkies/fuck_facebook.gif" alt="fuck_facebook.gif" /> <img src="./src/gifs/blinkies/graphics_by_gimp.gif" alt="graphics_by_gimp.gif" /> <img src="./src/gifs/blinkies/learn_html.gif" alt="learn_html.gif" /> <img src="./src/gifs/blinkies/leave-twitter.gif" alt="leave-twitter.gif" /><img src="./src/gifs/blinkies/stop_microsoft.gif" alt="stop_microsoft.gif" /> <img src="./src/gifs/blinkies/web-pi.png" alt="web-pi.png" /> <img src="./src/gifs/blinkies/piracy.gif" alt="piracy.gif" /> <img src="./src/gifs/blinkies/best_viewed_with_eyes.gif" alt="best_viewed_with_eyes.gif" /> <a href="https://spyware.neocities.org/articles/discord"><img src="./src/gifs/blinkies/discord-no-way-2.gif" alt="discord-no-way-2.gif" /></a> <a href="https://yesterweb.org/no-to-web3/"><img src="./src/gifs/blinkies/roly-saynotoweb3.gif" alt="roly-saynotoweb3.gif" /></a> -<a href="https://my.faith.rip/"><img src="./src/gifs/links/myfaithrip.gif" alt="myfaithrip.gif" /></a> -<a href="https://wiredcollective.neocities.org"><img src="./src/gifs/blinkies/wiredcollectivebutton.png" alt="wiredcollectivebutton.png" /></a> -<a href="https://razorback95.com"><img src="./src/gifs/blinkies/rz95_button.gif" alt="rz95_button.gif" /></a> -<a href="https://blueosmuseum.com"><img src="./src/gifs/blinkies/blueos_button.gif" alt="blueos_button.gif" /></a> -<img src="./src/gifs/blinkies/mafumafu.gif" alt="mafumafu.gif" /> -<img src="./src/gifs/blinkies/winxp.gif" alt="winxp.gif" /> -<img src="./src/gifs/blinkies/ihatems.gif" alt="ihatems.gif" /> -<img src="./src/gifs/blinkies/openbsdart.gif" alt="openbsdart.gif" /> -<img src="./src/gifs/blinkies/win10no.gif" alt="win10no.gif" /> -<img src="./src/gifs/blinkies/seedyourtorrents.gif" alt="seedyourtorrents.gif" /> -<img src="./src/gifs/blinkies/chrmevil.gif" alt="chrmevil.gif" /> -<img src="./src/gifs/blinkies/3dot5mmfc-button.gif" alt="3dot5mmfc-button.gif" /> -<img src="./src/gifs/blinkies/iecrash.gif" alt="iecrash.gif" /> -<img src="./src/gifs/blinkies/gregdock.gif" alt="gregdock.gif" /> -<a href="https://sapphic-cafe.neocities.org"><img src="./src/gifs/blinkies/sapphic-cafe-button.png" alt="sapphic-cafe-button.png" /></a> -<a href="https://neotomic.neocities.org/"><img src="./src/gifs/blinkies/neotomic.gif" alt="neotomic.gif" /></a> -<a href="https://openbsd.org/"><img src="./src/gifs/blinkies/openbsd.png" alt="openbsd.png" /></a> -<a href="https://partysepe13.neocities.org/"><img src="./src/gifs/blinkies/partysepe.png" alt="partysepe.png" /></a> -</p> -</div> -<div id="outline-container-orgbbd147a" class="outline-3"> -<h3 id="orgbbd147a">My banner</h3> -<div class="outline-text-3" id="text-orgbbd147a"> -<p> -If you enjoyed my website, you could link me on your personal website using this banner. If you don’t want to, then no pressure 💜 I still love you and I hope that this small shrine of mine will impress you in the future!!! -</p> - - -<div id="org1bfca51" class="figure"> -<p><img src="./src/gifs/crystal-tilde.gif" alt="crystal-tilde.gif" /> -</p> -</div> - -<div id="orgb59b9be" class="figure"> -<p><img src="./src/gifs/my_buttons/lain_crystal_glitch.gif" alt="lain_crystal_glitch.gif" width="240px" /> -</p> -</div> - -<p> -<i>And others too are in this directory <a href="./src/gifs/my_buttons/">./src/gifs/my_buttons/</a>. All of them were made by <a href="https://julians-art.neocities.org">https://julians-art.neocities.org</a></i> Thanks a lot Julian !!!/ -</p> -</div> -</div> -</div> -<div id="outline-container-org043e698" class="outline-2"> -<h2 id="org043e698"><a href="./links.html">Close this website, txEn eht nepO.( Webrings , so expect JavaScript on this page)!!</a></h2> -<div class="outline-text-2" id="text-org043e698"> -<p> -Geekring secret : 8e171c39-fb7c-465e-96df-bc110c9257f2 -</p> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2024-04-15 Mon 19:35</p> -</div> -</body> -</html> diff --git a/links.html b/links.html deleted file mode 100755 index 98cce8a..0000000 --- a/links.html +++ /dev/null @@ -1,106 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2023-11-10 Fri 11:11 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>Close this website, txEn eht nepO.(JavaScript ahead) 💜</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href="https://crystal.tilde.institute/"> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<div clas="glitch-container"> -<h1 class="title glitch"> -<span> - <b>Close this w<span class="red" style="color: #AD2128">e</span><span class="blue" style="color: #201E82">b</span>site, <div class="mirrored-text">Open the nExt</div>.</b> - </span> -</h1> -</div> -<div id="outline-container-orgcf6e5e0" class="outline-2"> -<h2 id="orgcf6e5e0">Webrings & Links</h2> -<div class="outline-text-2" id="text-orgcf6e5e0"> -<p> -<b>This site is a proud member of the geekring! Check some other geeky websites here!</b><br /> -</p> - -<p> -<a href="http://geekring.net/site/302/previous">Previous site</a> – <a href="http://geekring.net/site/301/random">Random Site</a> – <a href="http://geekring.net/site/301/next">Next Site</a><br /> -</p> - -<p> -<b>Do you long for a simpler time, when America was Online and the only person you could Ask was Jeeves? Hotline Webring is bringing that time back, with Webrings! <i>This website is part of the Hotline Webring</i></b><br /> -</p> - -<p> -<a href="https://hotlinewebring.club/crystal/previous">Previous site</a> – <a href="https://hotlinewebring.club/crystal/next">Next site</a><br /> -</p> -<iframe id="bucket-webring" style="width: 100%; height: 3rem; border: none;" src="https://webring.bucketfish.me/embed.html?name=crystal"></iframe> - -<link rel="stylesheet" -href="https://teethinvitro.neocities.org/webring/linuxring/script/onionring.css"> -<div id="transring"> -<script type="text/javascript" src="https://transring.neocities.org/onionring-variables.js"></script> -<script type="text/javascript" src="https://transring.neocities.org/onionring-widget.js"></script> -</div> - -<div id='linuxring'> -<script type="text/javascript" src="https://teethinvitro.neocities.org/webring/linuxring/script/onionring-variables.js"></script> -<script type="text/javascript" src="https://teethinvitro.neocities.org/webring/linuxring/script/onionring-widget.js"></script> -</div> -<table> -<tr> -<td><a href="https://webri.ng/webring/ladiesofthelinks/previous?via=https%3A%2F%2Fcrystal.tilde.institute"><img src="src/gifs/links/ladiesofthelinks/ladiesofthelink1.gif"></a></td> -<td><a href="https://ladiesofthe.link/"><img src="src/gifs/links/ladiesofthelinks/ladiesofthelink.gif"></a></td> -<td><a href="https://webri.ng/webring/ladiesofthelinks/next?via=https%3A%2F%2Fcrystal.tilde.institute"><img src="/src/gifs/links/ladiesofthelinks/ladiesofthelink2.gif"></a></td> -</tr> -</table> -</div> -<div id="outline-container-org8c1234f" class="outline-3"> -<h3 id="org8c1234f">Lainchan Webring</h3> -<div class="outline-text-3" id="text-org8c1234f"> -<p> -Lainring is a decentralized <a href="https://indieweb.org/webring">webring</a> created by the users of <a href="https://www.lainchan.org">Lainchan</a>, an anonymous image board. If you want to be added, go to the <a href="https://lainchan.org/%CE%A9/res/73638.html">Lainchan thread</a> and post your website there, together with a 240x60 button image.<br /> -</p> - - -<div id="lainring">... Loading, please wait ...</div> -<script> -document.addEventListener("DOMContentLoaded", function(event) { - /* Try to retrieve the json file */ - fetch('src/json/lainring.json').then(res => res.json()).then((data) => { - let out = ''; - /* For each element in the JSON, build an anchor-image DOM structure */ - data.items.forEach(element => { - /* This string is split in multiple lines for readability */ - out += '<a title="' + element.title + '" ' + - 'href="' + element.url + '">' + - '<img src="src/gifs/lainchan/' + element.img + '" alt="' + element.title + '" /></a>'; - }); - /* Inject the DOM structure into the element with the id 'lainring' */ - document.getElementById('lainring').innerHTML = out; - }).catch(err => { - /* throw an error */ - throw err - }); -}); -</script> -</div> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2023-11-10 Fri 11:11</p> -</div> -</body> -</html> \ No newline at end of file diff --git a/src/org/class_notes.html b/src/org/class_notes.html new file mode 100644 index 0000000..4f7a736 --- /dev/null +++ b/src/org/class_notes.html @@ -0,0 +1,420 @@ +<?xml version="1.0" encoding="utf-8"?> +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" +"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> +<head> +<!-- 2024-04-19 Fri 19:58 --> +<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> +<meta name="viewport" content="width=device-width, initial-scale=1" /> +<title>Class notes</title> +<meta name="author" content="Crystal" /> +<meta name="generator" content="Org Mode" /> +<style> + #content { max-width: 60em; margin: auto; } + .title { text-align: center; + margin-bottom: .2em; } + .subtitle { text-align: center; + font-size: medium; + font-weight: bold; + margin-top:0; } + .todo { font-family: monospace; color: red; } + .done { font-family: monospace; color: green; } + .priority { font-family: monospace; color: orange; } + .tag { background-color: #eee; font-family: monospace; + padding: 2px; font-size: 80%; font-weight: normal; } + .timestamp { color: #bebebe; } + .timestamp-kwd { color: #5f9ea0; } + .org-right { margin-left: auto; margin-right: 0px; text-align: right; } + .org-left { margin-left: 0px; margin-right: auto; text-align: left; } + .org-center { margin-left: auto; margin-right: auto; text-align: center; } + .underline { text-decoration: underline; } + #postamble p, #preamble p { font-size: 90%; margin: .2em; } + p.verse { margin-left: 3%; } + pre { + border: 1px solid #e6e6e6; + border-radius: 3px; + background-color: #f2f2f2; + padding: 8pt; + font-family: monospace; + overflow: auto; + margin: 1.2em; + } + pre.src { + position: relative; + overflow: auto; + } + pre.src:before { + display: none; + position: absolute; + top: -8px; + right: 12px; + padding: 3px; + color: #555; + background-color: #f2f2f299; + } + pre.src:hover:before { display: inline; margin-top: 14px;} + /* Languages per Org manual */ + pre.src-asymptote:before { content: 'Asymptote'; } + pre.src-awk:before { content: 'Awk'; } + pre.src-authinfo::before { content: 'Authinfo'; } + pre.src-C:before { content: 'C'; } + /* pre.src-C++ doesn't work in CSS */ + pre.src-clojure:before { content: 'Clojure'; } + pre.src-css:before { content: 'CSS'; } + pre.src-D:before { content: 'D'; } + pre.src-ditaa:before { content: 'ditaa'; } + pre.src-dot:before { content: 'Graphviz'; } + pre.src-calc:before { content: 'Emacs Calc'; } + pre.src-emacs-lisp:before { content: 'Emacs Lisp'; } + pre.src-fortran:before { content: 'Fortran'; } + pre.src-gnuplot:before { content: 'gnuplot'; } + pre.src-haskell:before { content: 'Haskell'; } + pre.src-hledger:before { content: 'hledger'; } + pre.src-java:before { content: 'Java'; } + pre.src-js:before { content: 'Javascript'; } + pre.src-latex:before { content: 'LaTeX'; } + pre.src-ledger:before { content: 'Ledger'; } + pre.src-lisp:before { content: 'Lisp'; } + pre.src-lilypond:before { content: 'Lilypond'; } + pre.src-lua:before { content: 'Lua'; } + pre.src-matlab:before { content: 'MATLAB'; } + pre.src-mscgen:before { content: 'Mscgen'; } + pre.src-ocaml:before { content: 'Objective Caml'; } + pre.src-octave:before { content: 'Octave'; } + pre.src-org:before { content: 'Org mode'; } + pre.src-oz:before { content: 'OZ'; } + pre.src-plantuml:before { content: 'Plantuml'; } + pre.src-processing:before { content: 'Processing.js'; } + pre.src-python:before { content: 'Python'; } + pre.src-R:before { content: 'R'; } + pre.src-ruby:before { content: 'Ruby'; } + pre.src-sass:before { content: 'Sass'; } + pre.src-scheme:before { content: 'Scheme'; } + pre.src-screen:before { content: 'Gnu Screen'; } + pre.src-sed:before { content: 'Sed'; } + pre.src-sh:before { content: 'shell'; } + pre.src-sql:before { content: 'SQL'; } + pre.src-sqlite:before { content: 'SQLite'; } + /* additional languages in org.el's org-babel-load-languages alist */ + pre.src-forth:before { content: 'Forth'; } + pre.src-io:before { content: 'IO'; } + pre.src-J:before { content: 'J'; } + pre.src-makefile:before { content: 'Makefile'; } + pre.src-maxima:before { content: 'Maxima'; } + pre.src-perl:before { content: 'Perl'; } + pre.src-picolisp:before { content: 'Pico Lisp'; } + pre.src-scala:before { content: 'Scala'; } + pre.src-shell:before { content: 'Shell Script'; } + pre.src-ebnf2ps:before { content: 'ebfn2ps'; } + /* additional language identifiers per "defun org-babel-execute" + in ob-*.el */ + pre.src-cpp:before { content: 'C++'; } + pre.src-abc:before { content: 'ABC'; } + pre.src-coq:before { content: 'Coq'; } + pre.src-groovy:before { content: 'Groovy'; } + /* additional language identifiers from org-babel-shell-names in + ob-shell.el: ob-shell is the only babel language using a lambda to put + the execution function name together. */ + pre.src-bash:before { content: 'bash'; } + pre.src-csh:before { content: 'csh'; } + pre.src-ash:before { content: 'ash'; } + pre.src-dash:before { content: 'dash'; } + pre.src-ksh:before { content: 'ksh'; } + pre.src-mksh:before { content: 'mksh'; } + pre.src-posh:before { content: 'posh'; } + /* Additional Emacs modes also supported by the LaTeX listings package */ + pre.src-ada:before { content: 'Ada'; } + pre.src-asm:before { content: 'Assembler'; } + pre.src-caml:before { content: 'Caml'; } + pre.src-delphi:before { content: 'Delphi'; } + pre.src-html:before { content: 'HTML'; } + pre.src-idl:before { content: 'IDL'; } + pre.src-mercury:before { content: 'Mercury'; } + pre.src-metapost:before { content: 'MetaPost'; } + pre.src-modula-2:before { content: 'Modula-2'; } + pre.src-pascal:before { content: 'Pascal'; } + pre.src-ps:before { content: 'PostScript'; } + pre.src-prolog:before { content: 'Prolog'; } + pre.src-simula:before { content: 'Simula'; } + pre.src-tcl:before { content: 'tcl'; } + pre.src-tex:before { content: 'TeX'; } + pre.src-plain-tex:before { content: 'Plain TeX'; } + pre.src-verilog:before { content: 'Verilog'; } + pre.src-vhdl:before { content: 'VHDL'; } + pre.src-xml:before { content: 'XML'; } + pre.src-nxml:before { content: 'XML'; } + /* add a generic configuration mode; LaTeX export needs an additional + (add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */ + pre.src-conf:before { content: 'Configuration File'; } + + table { border-collapse:collapse; } + caption.t-above { caption-side: top; } + caption.t-bottom { caption-side: bottom; } + td, th { vertical-align:top; } + th.org-right { text-align: center; } + th.org-left { text-align: center; } + th.org-center { text-align: center; } + td.org-right { text-align: right; } + td.org-left { text-align: left; } + td.org-center { text-align: center; } + dt { font-weight: bold; } + .footpara { display: inline; } + .footdef { margin-bottom: 1em; } + .figure { padding: 1em; } + .figure p { text-align: center; } + .equation-container { + display: table; + text-align: center; + width: 100%; + } + .equation { + vertical-align: middle; + } + .equation-label { + display: table-cell; + text-align: right; + vertical-align: middle; + } + .inlinetask { + padding: 10px; + border: 2px solid gray; + margin: 10px; + background: #ffffcc; + } + #org-div-home-and-up + { text-align: right; font-size: 70%; white-space: nowrap; } + textarea { overflow-x: auto; } + .linenr { font-size: smaller } + .code-highlighted { background-color: #ffff00; } + .org-info-js_info-navigation { border-style: none; } + #org-info-js_console-label + { font-size: 10px; font-weight: bold; white-space: nowrap; } + .org-info-js_search-highlight + { background-color: #ffff00; color: #000000; font-weight: bold; } + .org-svg { } +</style> +</head> +<body> +<div id="content" class="content"> +<h1 class="title">Class notes</h1> +<div id="table-of-contents" role="doc-toc"> +<h2>Table of Contents</h2> +<div id="text-table-of-contents" role="doc-toc"> +<ul> +<li><a href="#org740344c">1. class 1 <i>sun sep 17 13:04:43 2023</i></a> +<ul> +<li><a href="#orgdeedad1">1.1. Les Reseaux locaux (LAN)</a></li> +<li><a href="#org4046b4b">1.2. MAC Address :</a></li> +<li><a href="#orgc7732e1">1.3. RJ-45 connecteurs</a></li> +<li><a href="#org0f55269">1.4. IPV4 classes :</a></li> +<li><a href="#org4127e6b">1.5. Adresses privées:</a></li> +<li><a href="#orge90d8a0">1.6. 500 hosts :</a></li> +<li><a href="#org67a8bc7">1.7. 150 hosts :</a></li> +<li><a href="#orgea65848">1.8. 60 hosts :</a></li> +<li><a href="#org9afb58b">1.9. 30 hosts:</a></li> +<li><a href="#orge54390c">1.10. 20</a></li> +<li><a href="#orgd72daa2">1.11. 15</a></li> +</ul> +</li> +<li><a href="#orgc3dfb36">2. Class 2Sun <i>Sep 24 09:09:28 2023</i></a> +<ul> +<li><a href="#org7607698">2.1. CCTV (finally)</a></li> +</ul> +</li> +</ul> +</div> +</div> + + +<div id="outline-container-org740344c" class="outline-2"> +<h2 id="org740344c"><span class="section-number-2">1.</span> class 1 <i>sun sep 17 13:04:43 2023</i></h2> +<div class="outline-text-2" id="text-1"> +</div> +<div id="outline-container-orgdeedad1" class="outline-3"> +<h3 id="orgdeedad1"><span class="section-number-3">1.1.</span> Les Reseaux locaux (LAN)</h3> +<div class="outline-text-3" id="text-1-1"> +<p> +Cable 10 mbps ou moins = Ethernet +Cable 100 mbps = Fast Ethernet +Cable 1000 mbps ou plus = Giga Ethernet +</p> +</div> +</div> + +<div id="outline-container-org4046b4b" class="outline-3"> +<h3 id="org4046b4b"><span class="section-number-3">1.2.</span> MAC Address :</h3> +<div class="outline-text-3" id="text-1-2"> +<p> +First three Bytes : vendor +Last three Bytes : Unique ID +(In Hexadecimal) +</p> + +<p> +TODO: CSMA/ CA CD +</p> +</div> +</div> + +<div id="outline-container-orgc7732e1" class="outline-3"> +<h3 id="orgc7732e1"><span class="section-number-3">1.3.</span> RJ-45 connecteurs</h3> +<div class="outline-text-3" id="text-1-3"> +</div> +<ol class="org-ol"> +<li><a id="org4039adc"></a>Straight<br /></li> +<li><a id="orgea66000"></a>Crossover (croisé)<br /></li> +<li><a id="orgfd2e4fe"></a>Rollover (console)<br /></li> +</ol> +</div> + +<div id="outline-container-org0f55269" class="outline-3"> +<h3 id="org0f55269"><span class="section-number-3">1.4.</span> IPV4 classes :</h3> +<div class="outline-text-3" id="text-1-4"> +<ul class="org-ul"> +<li>Classe A : 0 - 127 /8 +<ul class="org-ul"> +<li>0.0.0.0/0 : route par default</li> +<li>127.0.0.0/8 : bouclage</li> +</ul></li> +<li>Classe B : 128 - 191 /16 +<ul class="org-ul"> +<li>169.254.0.0/16 : APIPA</li> +</ul></li> +<li>Classe C : 192 - 223 /24</li> +<li>Classe D : 224 - 239 +<ul class="org-ul"> +<li>Multicast</li> +</ul></li> +<li>Classe E : 240 - 255</li> +</ul> +</div> +</div> + +<div id="outline-container-org4127e6b" class="outline-3"> +<h3 id="org4127e6b"><span class="section-number-3">1.5.</span> Adresses privées:</h3> +<div class="outline-text-3" id="text-1-5"> +<ul class="org-ul"> +<li>Classe A : 10.0.0.0 - 10.255.255.255 /8</li> +<li>Classe B : 172.16.0.0 - 172.31.255.255 /12</li> +<li>Classe C : 192.168.0.0 - 192.168.255.255 /16</li> +</ul> + + +<p> +8 7 6 5 4 3 2 1 +128 64 32 16 8 4 2 1 +256 128 64 32 16 8 4 2 +/24 /25 /26 /27 /28 /29 /30 /31 +</p> + +<p> +500 +150 +60 +30 +20 +15 +</p> +</div> +</div> +<div id="outline-container-orge90d8a0" class="outline-3"> +<h3 id="orge90d8a0"><span class="section-number-3">1.6.</span> 500 hosts :</h3> +<div class="outline-text-3" id="text-1-6"> +<p> +Addresse: 10.0.0.0 /23 +</p> + +<p> +500 - 256 = 244 +</p> + +<p> +First IP : 10.0.0.1 /23 +Last IP : 10.0.1.254 /23 +@B IP : 10.0.1.255 /23 +Mask : 255.255.254.0 +</p> +</div> +</div> + +<div id="outline-container-org67a8bc7" class="outline-3"> +<h3 id="org67a8bc7"><span class="section-number-3">1.7.</span> 150 hosts :</h3> +<div class="outline-text-3" id="text-1-7"> +<p> +Addresse: 10.0.2.0 /24 +First IP: 10.0.2.1 /24 +Last IP: 10.0.2.254 /24 +@B IP: 10.0.2.255 /24 +Mask: 255.255.255.0 +</p> +</div> +</div> + +<div id="outline-container-orgea65848" class="outline-3"> +<h3 id="orgea65848"><span class="section-number-3">1.8.</span> 60 hosts :</h3> +<div class="outline-text-3" id="text-1-8"> +<p> +Addresse: 10.0.3.0 /26 +First IP: 10.0.3.1 /26 +Last IP: 10.0.3.63 /26 +@B IP: 10.0.3.64 /26 +Mask: 255.255.255.191 +</p> +</div> +</div> + +<div id="outline-container-org9afb58b" class="outline-3"> +<h3 id="org9afb58b"><span class="section-number-3">1.9.</span> 30 hosts:</h3> +<div class="outline-text-3" id="text-1-9"> +<p> +Addresse: 10.0.3.63/8 +First IP: 10.0.3.64/8 +Last IP: 10.0.3.96/8 +@B IP: 10.0.3.97/8 +Mask: 255.255.255.158/11 +</p> +</div> +</div> + +<div id="outline-container-orge54390c" class="outline-3"> +<h3 id="orge54390c"><span class="section-number-3">1.10.</span> 20</h3> +<div class="outline-text-3" id="text-1-10"> +<p> +Addresse: 10.0.3.97/8 +First IP: 10.0.3.98/8 +Last IP: 10.0.3.128/8 +@B IP: 10.0.3.129/8 +Mask: 255.255.255.126/11 +</p> +</div> +</div> +<div id="outline-container-orgd72daa2" class="outline-3"> +<h3 id="orgd72daa2"><span class="section-number-3">1.11.</span> 15</h3> +<div class="outline-text-3" id="text-1-11"> +<p> +Addresse: 10.0.3.129/8 +First IP: 10.0.3.130/8 +Last IP: 10.0.3.144/8 +@B IP: 10.0.3.145/8 +Mask: 255.255.255.110/12 +</p> +</div> +</div> +</div> + +<div id="outline-container-orgc3dfb36" class="outline-2"> +<h2 id="orgc3dfb36"><span class="section-number-2">2.</span> Class 2Sun <i>Sep 24 09:09:28 2023</i></h2> +<div class="outline-text-2" id="text-2"> +</div> +<div id="outline-container-org7607698" class="outline-3"> +<h3 id="org7607698"><span class="section-number-3">2.1.</span> CCTV (finally)</h3> +</div> +</div> +</div> +<div id="postamble" class="status"> +<p class="author">Author: Crystal</p> +<p class="date">Created: 2024-04-19 Fri 19:58</p> +<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> +</div> +</body> +</html> diff --git a/src/org/export.sh b/src/org/export.sh new file mode 100755 index 0000000..a6ca475 --- /dev/null +++ b/src/org/export.sh @@ -0,0 +1,8 @@ +#!/usr/local/bin/bash + +# Set the directory to search (replace with your actual path) +TARGET_DIR="." + +# Function to process each .org file +# Find all .org files recursively +find "$TARGET_DIR" -type f -name "*.org" -exec emacs {} --batch -f org-html-export-to-html --kill \; diff --git a/super_secret.html b/super_secret.html deleted file mode 100755 index 1bc8695..0000000 --- a/super_secret.html +++ /dev/null @@ -1,38 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2023-09-10 Sun 19:11 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>SUPER SECRET WEBSITE</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="src/css/style.css"/> -</head> -<body> -<div id="content" class="content"> -<h1 class="title">SUPER SECRET WEBSITE</h1> -<div class="smurf"> - - -<div id="org6b38aea" class="figure"> -<p><img src="./src/gifs/smurf.jpg" alt="smurf.jpg" /> -</p> -</div> -</div> - - -<audio controls autoplay loop> - <source src="./src/media/welive.mp3" type="audio/mpeg"> - Your browser does not support the audio element. -</audio> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2023-09-10 Sun 19:11</p> -</div> -</body> -</html> \ No newline at end of file diff --git a/uni_notes/algebra.html b/uni_notes/algebra.html deleted file mode 100755 index 0e223c5..0000000 --- a/uni_notes/algebra.html +++ /dev/null @@ -1,1870 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2023-11-01 Wed 20:17 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>Algebra 1</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="https://crystal.tilde.institute/favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href="../../../uni_notes/"> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title">Algebra 1</h1> -<div id="table-of-contents" role="doc-toc"> -<h2>Table of Contents</h2> -<div id="text-table-of-contents" role="doc-toc"> -<ul> -<li><a href="#org42f27fc">Contenu de la Matiére</a> -<ul> -<li><a href="#orgf20cf94">Rappels et compléments (11H)</a></li> -<li><a href="#orgf700058">Structures Algébriques (11H)</a></li> -<li><a href="#org7a29a82">Polynômes et fractions rationnelles</a></li> -</ul> -</li> -<li><a href="#org7207cb0">Premier cours : Logique mathématique et méthodes du raisonnement mathématique <i>Sep 25</i> :</a> -<ul> -<li><a href="#orgb936329">Properties:</a> -<ul> -<li><a href="#orgf5da498"><b>Absorption</b>:</a></li> -<li><a href="#org49dbf9d"><b>Commutativity</b>:</a></li> -<li><a href="#orge255044"><b>Associativity</b>:</a></li> -<li><a href="#org31cc6c8"><b>Distributivity</b>:</a></li> -<li><a href="#orgf861930"><b>Neutral element</b>:</a></li> -<li><a href="#org8cb6e02"><b>Negation of a conjunction & a disjunction</b>:</a></li> -<li><a href="#orgfe01ac7"><b>Transitivity</b>:</a></li> -<li><a href="#org976f527"><b>Contraposition</b>:</a></li> -<li><a href="#org0865f2b">God only knows what this property is called:</a></li> -</ul> -</li> -<li><a href="#org316b141">Some exercices I found online :</a> -<ul> -<li><a href="#orga3825f4">USTHB 2022/2023 Section B :</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#org21d6c03">2éme cours <i>Oct 2</i></a> -<ul> -<li><a href="#orgd6c9f49">Quantifiers</a> -<ul> -<li><a href="#orgb332b43">Proprieties</a></li> -</ul> -</li> -<li><a href="#orged685c1">Multi-parameter proprieties :</a></li> -<li><a href="#org78d7ed0">Methods of mathematical reasoning :</a> -<ul> -<li><a href="#org7d21c38">Direct reasoning :</a></li> -<li><a href="#orgcfd8723">Reasoning by the Absurd:</a></li> -<li><a href="#org102d3fa">Reasoning by contraposition:</a></li> -<li><a href="#org81cb388">Reasoning by counter example:</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#orgc2178b8">3eme Cours : <i>Oct 9</i></a> -<ul> -<li> -<ul> -<li><a href="#org4855f6f">Reasoning by recurrence :</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#orgde6bfac">4eme Cours : Chapitre 2 : Sets and Operations</a> -<ul> -<li><a href="#orgfe8000a">Definition of a set :</a></li> -<li><a href="#orgfe04671">Belonging, inclusion, and equality :</a></li> -<li><a href="#orga2eb99d">Intersections and reunions :</a> -<ul> -<li><a href="#org560d563">Intersection:</a></li> -<li><a href="#org7147bc3">Union:</a></li> -<li><a href="#org16b5ab2">Difference between two sets:</a></li> -<li><a href="#orgdac190b">Complimentary set:</a></li> -<li><a href="#org4e0b111">Symmetrical difference</a></li> -</ul> -</li> -<li><a href="#org691c863">Proprieties :</a> -<ul> -<li><a href="#org9cc9f31">Commutativity:</a></li> -<li><a href="#org471083b">Associativity:</a></li> -<li><a href="#orge63be10">Distributivity:</a></li> -<li><a href="#orgfb01947">Lois de Morgan:</a></li> -<li><a href="#orge1a41eb">An other one:</a></li> -<li><a href="#org9939b0f">An other one:</a></li> -<li><a href="#org90bfdc4">And an other one:</a></li> -<li><a href="#org1e49001">And the last one:</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#org272eca3">5eme cours: L’ensemble des parties d’un ensemble <i>Oct 16</i></a> -<ul> -<li> -<ul> -<li><a href="#org5b29e32">Notes :</a></li> -<li><a href="#org5636bd8">Examples :</a></li> -</ul> -</li> -<li><a href="#orgd8cb2c3">Partition of a set :</a></li> -<li><a href="#orgf40404d">Cartesian products :</a> -<ul> -<li><a href="#orgd526cb8">Example :</a></li> -<li><a href="#org56dd088">Some proprieties:</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#org5ee4278">Binary relations in a set :</a> -<ul> -<li><a href="#orgddc9af6">Definition :</a></li> -<li><a href="#orge65424e">Proprieties :</a></li> -<li><a href="#orgd7877d3">Equivalence relationship :</a> -<ul> -<li><a href="#org85cf025">Equivalence class :</a></li> -</ul> -</li> -<li><a href="#orge18dcc7">Order relationship :</a> -<ul> -<li><a href="#org60d471a"><span class="todo TODO">TODO</span> Examples :</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#org77de6e3">TP exercices <i>Oct 20</i> :</a> -<ul> -<li><a href="#org3ca8006">Exercice 3 :</a> -<ul> -<li><a href="#orgad95ec3">Question 3</a></li> -</ul> -</li> -<li><a href="#org8180ae0">Exercice 4 :</a> -<ul> -<li><a href="#orgfe0b1e2"><span class="done DONE">DONE</span> Question 1 :</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#org2d6e0ba">Chapter 3 : Applications</a> -<ul> -<li><a href="#orga5be12f">3.1 Generalities about applications :</a> -<ul> -<li><a href="#org805d7bc">Definition :</a></li> -<li><a href="#org7947331">Restriction and prolongation of an application :</a></li> -<li><a href="#orgd94bc69">Composition of applications :</a></li> -</ul> -</li> -<li><a href="#org257d05a">3.2 Injection, surjection and bijection :</a> -<ul> -<li><a href="#org1612e09">Proposition :</a></li> -</ul> -</li> -<li><a href="#orgebdf518">3.3 Reciprocal applications :</a> -<ul> -<li><a href="#orgf072e42">Def :</a></li> -<li><a href="#org244b352">Theorem :</a></li> -<li><a href="#org1479c0e">Some proprieties :</a></li> -</ul> -</li> -<li><a href="#orgaf81bb3">3.4 Direct Image and reciprocal Image :</a> -<ul> -<li><a href="#org87b91e2">Direct Image :</a></li> -<li><a href="#org500bc40">Reciprocal image :</a></li> -</ul> -</li> -</ul> -</li> -</ul> -</div> -</div> -<div id="outline-container-org42f27fc" class="outline-2"> -<h2 id="org42f27fc">Contenu de la Matiére</h2> -<div class="outline-text-2" id="text-org42f27fc"> -</div> -<div id="outline-container-orgf20cf94" class="outline-3"> -<h3 id="orgf20cf94">Rappels et compléments (11H)</h3> -<div class="outline-text-3" id="text-orgf20cf94"> -<ul class="org-ul"> -<li>Logique mathématique et méthodes du raisonnement mathématique<br /></li> -<li>Ensembles et Relations<br /></li> -<li>Applications<br /></li> -</ul> -</div> -</div> -<div id="outline-container-orgf700058" class="outline-3"> -<h3 id="orgf700058">Structures Algébriques (11H)</h3> -<div class="outline-text-3" id="text-orgf700058"> -<ul class="org-ul"> -<li>Groupes et morphisme de groupes<br /></li> -<li>Anneaux et morphisme d’anneaux<br /></li> -<li>Les corps<br /></li> -</ul> -</div> -</div> -<div id="outline-container-org7a29a82" class="outline-3"> -<h3 id="org7a29a82">Polynômes et fractions rationnelles</h3> -<div class="outline-text-3" id="text-org7a29a82"> -<ul class="org-ul"> -<li>Notion du polynôme à une indéterminée á coefficients dans un anneau<br /></li> -<li>Opérations Algébriques sur les polynômes<br /></li> -<li>Arithmétique dans l’anneau des polynômes<br /></li> -<li>Polynôme dérivé et formule de Taylor<br /></li> -<li>Notion de racine d’un polynôme<br /></li> -<li>Notion de Fraction rationelle á une indéterminée<br /></li> -<li>Décomposition des fractions rationelles en éléments simples<br /></li> -</ul> -</div> -</div> -</div> -<div id="outline-container-org7207cb0" class="outline-2"> -<h2 id="org7207cb0">Premier cours : Logique mathématique et méthodes du raisonnement mathématique <i>Sep 25</i> :</h2> -<div class="outline-text-2" id="text-org7207cb0"> -<p> -Let <b>P</b> <b>Q</b> and <b>R</b> be propositions which can either be <b>True</b> or <b>False</b>. And let’s also give the value <b>1</b> to each <b>True</b> proposition and <b>0</b> to each false one.<br /> -</p> - -<p> -<i>Ex:</i><br /> -</p> -<ul class="org-ul"> -<li><b>5 ≥ 2</b> is a proposition, a correct one !!!<br /></li> -<li><b>The webmaster is a girl</b> is also a proposition, which is also correct.<br /></li> -<li><b>x is always bigger than 5</b> is <b>not</b> a proposition, because we CAN’T determine if it’s correct or not as <b>x</b> changes.<br /></li> -</ul> -<p> -…etc<br /> -</p> - -<p> -In order to avoid repetition, and rewriting the proposition over and over, we just assign a capital letter to them such as <b>P Q</b> or <b>R</b>.<br /> -</p> - -<p> -So now we could write :<br /> -<b>Let the proposition P be 5 ≥ 2, we notice that P is always True, therefor its validity is 1</b><br /> -</p> - -<p> -We also have the opposite of <b>P</b>, which is <b>not(P)</b> but for simplicity we use <b>P̅</b> (A P with a bar on top, in case it doesn’t load for you), now let’s go back to the previous example:<br /> -</p> - -<p> -<b>Since we know that the proposition P is true, we can conclude that P̅ is false. As P and P̅ can NOT be true at the same time. It’s like saying 5 is greater and also lesser than 2…doesn’t make sense, does it ?</b><br /> -</p> - -<p> -Now let’s say we have two propositions, and we want to test the validity of their disjunction….. Okay what is this “disjunction” ? <b>Great Question Billy !!!</b> A disjunction is true if either propositions are true<br /> -</p> - -<p> -Ex:<br /> -<b>Let proposition P be “The webmaster is asleep”, and Q be “The reader loves pufferfishes”. The disjunction of these two propositions can have 4 different values showed in this Table of truth (such a badass name):</b><br /> -</p> - -<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> - - -<colgroup> -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> -</colgroup> -<thead> -<tr> -<th scope="col" class="org-right">P</th> -<th scope="col" class="org-right">Q</th> -<th scope="col" class="org-right">Disjunction</th> -</tr> -</thead> -<tbody> -<tr> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -</tr> -</tbody> -</table> - -<p> -<i>What the hell is this ?</i><br /> -The first colomn is equivalent to saying : “The webmaster is asleep AND The reader loves pufferfishes”<br /> -The second one means : “The webmaster is asleep AND The reader DOESN’T love pufferfishes (if you are in this case, then <b>I HATE YOU</b>)”<br /> -The third one… <i>zzzzzzz</i><br /> -</p> - -<p> -You got the idea !!!<br /> -And since we are talking about a disjunction here, <b>one of the propositions</b> need to be true in order for this disjunction to be true.<br /> -</p> - -<p> -You may be wondering…. Crystal, can’t we write a disjunction in magical math symbols ? And to this I respond with a big <b>YES</b>. A disjunction is symbolized by a <b>∨</b> . So the disjunction between proposition <b>P & Q</b> can be written this way : <b>P ∨ Q</b><br /> -</p> - -<p> -What if, we want to test whether or not two propositions are true AT THE SAME TIME ? Long story short, we can, it’s called a conjunction, same concept, as before, only this time the symbol is <b>P ∧ Q</b>, and is only true if <b>P</b> and <b>Q</b> are true. So we get a Table like this :<br /> -</p> - -<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> - - -<colgroup> -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> -</colgroup> -<thead> -<tr> -<th scope="col" class="org-right">P</th> -<th scope="col" class="org-right">Q</th> -<th scope="col" class="org-right">P ∨ Q</th> -<th scope="col" class="org-right">P ∧ Q</th> -</tr> -</thead> -<tbody> -<tr> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -</tr> - -<tr> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -</tr> - -<tr> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -</tr> -</tbody> -</table> - -<p> -<b>Always remember: 1 means true and 0 means false</b><br /> -</p> - -<p> -There are two more basics to cover here before going to some properties, the first one is implication symbolized by the double arrow <b>⇒</b><br /> -</p> - -<p> -Implication is kinda hard for my little brain to explain, so I will just say what it means:<br /> -</p> - -<p> -<b>If P implies Q, this means that either Q, or the opposite of P are correct</b><br /> -</p> - -<p> -or in math terms<br /> -</p> - -<p> -<b>P ⇒ Q translates to P̅ ∨ Q</b><br /> -Let’s illustrate :<br /> -</p> - -<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> - - -<colgroup> -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> -</colgroup> -<thead> -<tr> -<th scope="col" class="org-right">P</th> -<th scope="col" class="org-right">Q</th> -<th scope="col" class="org-right">P̅</th> -<th scope="col" class="org-right">Q̅</th> -<th scope="col" class="org-right">P ∨ Q</th> -<th scope="col" class="org-right">P ∧ Q</th> -<th scope="col" class="org-right">P ⇒ Q (P̅ ∨ Q)</th> -</tr> -</thead> -<tbody> -<tr> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -</tr> - -<tr> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -</tr> -</tbody> -</table> - -<p> -<b>If you look clearly, there is only one case where an implication is false. therefor you just need to find it, and blindly say that the others are correct. A rule of thumb is that: “A correct never implies a false”, or “If a 1 tries to imply a 0, the implication is a 0”</b><br /> -</p> - -<p> -Aight, a last one and we are done!!! Equivalence, which is fairly easy, symbolized by a <b>⇔</b> symbol.<br /> -</p> - -<p> -A proposition is equivalent to another only when both of them have <b>the same value of truth</b> AKA: both true or both false. a little table will help demonstrate what i mean.<br /> -</p> - -<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> - - -<colgroup> -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> -</colgroup> -<thead> -<tr> -<th scope="col" class="org-right">P</th> -<th scope="col" class="org-right">Q</th> -<th scope="col" class="org-right">P̅</th> -<th scope="col" class="org-right">Q̅</th> -<th scope="col" class="org-right">P ∨ Q</th> -<th scope="col" class="org-right">P ∧ Q</th> -<th scope="col" class="org-right">P ⇒ Q (P̅ ∨ Q)</th> -<th scope="col" class="org-right">P ⇔ Q</th> -</tr> -</thead> -<tbody> -<tr> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -</tr> - -<tr> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -</tr> - -<tr> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -</tr> -</tbody> -</table> - -<p> -<i>Note: P implying Q is equivalent to P̅ implying Q̅, or: (P ⇒ Q) ⇔ (P̅ ⇒ Q̅)</i><br /> -</p> -</div> -<div id="outline-container-orgb936329" class="outline-3"> -<h3 id="orgb936329">Properties:</h3> -<div class="outline-text-3" id="text-orgb936329"> -</div> -<div id="outline-container-orgf5da498" class="outline-4"> -<h4 id="orgf5da498"><b>Absorption</b>:</h4> -<div class="outline-text-4" id="text-orgf5da498"> -<p> -(P ∨ P) ⇔ P<br /> -</p> - -<p> -(P ∧ P) ⇔ P<br /> -</p> -</div> -</div> -<div id="outline-container-org49dbf9d" class="outline-4"> -<h4 id="org49dbf9d"><b>Commutativity</b>:</h4> -<div class="outline-text-4" id="text-org49dbf9d"> -<p> -(P ∧ Q) ⇔ (Q ∧ P)<br /> -</p> - -<p> -(P ∨ Q) ⇔ (Q ∨ P)<br /> -</p> -</div> -</div> -<div id="outline-container-orge255044" class="outline-4"> -<h4 id="orge255044"><b>Associativity</b>:</h4> -<div class="outline-text-4" id="text-orge255044"> -<p> -P ∧ (Q ∧ R) ⇔ (P ∧ Q) ∧ R<br /> -</p> - -<p> -P ∨ (Q ∨ R) ⇔ (P ∨ Q) ∨ R<br /> -</p> -</div> -</div> -<div id="outline-container-org31cc6c8" class="outline-4"> -<h4 id="org31cc6c8"><b>Distributivity</b>:</h4> -<div class="outline-text-4" id="text-org31cc6c8"> -<p> -P ∧ (Q ∨ R) ⇔ (P ∧ Q) ∨ (P ∧ R)<br /> -</p> - -<p> -P ∨ (Q ∧ R) ⇔ (P ∨ Q) ∧ (P ∨ R)<br /> -</p> -</div> -</div> -<div id="outline-container-orgf861930" class="outline-4"> -<h4 id="orgf861930"><b>Neutral element</b>:</h4> -<div class="outline-text-4" id="text-orgf861930"> -<p> -<i>We define proposition <b>T</b> to be always <b>true</b> and <b>F</b> to be always <b>false</b></i><br /> -</p> - -<p> -P ∧ T ⇔ P<br /> -</p> - -<p> -P ∨ F ⇔ P<br /> -</p> -</div> -</div> -<div id="outline-container-org8cb6e02" class="outline-4"> -<h4 id="org8cb6e02"><b>Negation of a conjunction & a disjunction</b>:</h4> -<div class="outline-text-4" id="text-org8cb6e02"> -<p> -Now we won’t use bars here because my lazy ass doesn’t know how, so instead I will use not()!!!<br /> -</p> - -<p> -not(<b>P ∧ Q</b>) ⇔ P̅ ∨ Q̅<br /> -</p> - -<p> -not(<b>P ∨ Q</b>) ⇔ P̅ ∧ Q̅<br /> -</p> - -<p> -<b>A rule I really like to use here is: Break and Invert. Basically you break the bar into the three characters of the propositions, so you get not(P) not(∧ or ∨) <i>NOT AN ACTUAL MATH WRITING. DONT USE IT ANYWHERE ELSE OTHER THAN YOUR BRAIN</i> and not(Q)</b><br /> -</p> -</div> -</div> -<div id="outline-container-orgfe01ac7" class="outline-4"> -<h4 id="orgfe01ac7"><b>Transitivity</b>:</h4> -<div class="outline-text-4" id="text-orgfe01ac7"> -<p> -[(P ⇒ Q) AND (Q ⇒ R)] ⇔ P ⇒ R<br /> -</p> -</div> -</div> -<div id="outline-container-org976f527" class="outline-4"> -<h4 id="org976f527"><b>Contraposition</b>:</h4> -<div class="outline-text-4" id="text-org976f527"> -<p> -(P ⇒ Q) ⇔ (Q̅ ⇒ P̅)<br /> -</p> -</div> -</div> -<div id="outline-container-org0865f2b" class="outline-4"> -<h4 id="org0865f2b">God only knows what this property is called:</h4> -<div class="outline-text-4" id="text-org0865f2b"> -<p> -<i>If</i><br /> -</p> - -<p> -(P ⇒ Q) is true<br /> -</p> - -<p> -and<br /> -</p> - -<p> -(P̅ ⇒ Q) is true<br /> -</p> - -<p> -then<br /> -</p> - -<p> -Q is always true<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org316b141" class="outline-3"> -<h3 id="org316b141">Some exercices I found online :</h3> -<div class="outline-text-3" id="text-org316b141"> -</div> -<div id="outline-container-orga3825f4" class="outline-4"> -<h4 id="orga3825f4">USTHB 2022/2023 Section B :</h4> -<div class="outline-text-4" id="text-orga3825f4"> -</div> -<ul class="org-ul"> -<li><a id="orge27aa8d"></a>Exercice 1: Démontrer les équivalences suivantes:<br /> -<div class="outline-text-5" id="text-orge27aa8d"> -<ol class="org-ol"> -<li><p> -(P ⇒ Q) ⇔ (Q̅ ⇒ P̅)<br /> -</p> - -<p> -Basically we are asked to prove contraposition, so here we have ( P ⇒ Q ) which is equivalent to P̅ ∨ Q <b>By definition : (P ⇒ Q) ⇔ (P̅ ∨ Q)</b><br /> -</p></li> -</ol> - - -<p> -So we end up with : <b>(P̅ ∨ Q) ⇔ (Q̅ ⇒ P̅)</b>, now we just do the same with the second part of the contraposition. <b>(Q̅ ⇒ P̅) ⇔ (Q ∨ P̅)</b> therefor :<br /> -</p> - - -<p> -<b>(Q ∨ P̅) ⇔ (P̅ ∨ Q)</b>, which is true because of commutativity<br /> -</p> - -<ol class="org-ol"> -<li>not(P ⇒ Q) ⇔ P ∧ Q̅<br /></li> -</ol> - - -<p> -Okaaaay so, let’s first get rid of the implication, because I don’t like it : <b>not(P̅ ∨ Q)</b><br /> -</p> - - -<p> -Now that we got rid of it, we can negate the whole disjunction <b>not(P̅ ∨ Q) ⇔ (P ∧ Q̅)</b>. Which is the equivalence we needed to prove<br /> -</p> - -<ol class="org-ol"> -<li><p> -P ⇒ (Q ∧ R) ⇔ (P ⇒ Q) ∧ (P ⇒ R)<br /> -</p> - -<p> -One might be tempted to replace P with P̅ to get rid of the implication…sadly this isnt it. All we have to do here is resort to <b>Distributivity</b>, because yeah, we can distribute an implication across a {con/dis}junction<br /> -</p></li> - -<li><p> -P ∧ (Q ∨ R) ⇔ (P ∧ Q) ∨ (P ∧ R)<br /> -</p> - -<p> -Literally the same as above 🩷<br /> -</p></li> -</ol> -</div> -</li> -<li><a id="orgd9c7023"></a>Exercice 2: Dire si les propositions suivantes sont vraies ou fausses, et les nier:<br /> -<div class="outline-text-5" id="text-orgd9c7023"> -<ol class="org-ol"> -<li><p> -∀x ∈ ℝ ,∃y ∈ ℝ*+, tels que e^x = y<br /> -</p> - -<p> -For each x from the set of Real numbers, there exists a number y from the set of non-zero positive Real numbers that satisfies the equation : e^x = y<br /> -</p></li> -</ol> - - -<p> -“The function f(x)=e^x is always positive and non-null”, the very definition of an exponential function !!!!<br /> -</p> - - -<p> -<b>So the proposition is true</b><br /> -</p> - - -<ol class="org-ol"> -<li>∃x ∈ ℝ, tels que x^2 < x < x^3<br /></li> -</ol> - - -<p> -We just need to find a value that satisifies this condition…thankfully its easy….<br /> -</p> - -<p> -x² < x < x³ , we divide the three terms by x so we get :<br /> -</p> - - -<p> -x < 1 < x² , or :<br /> -</p> - - -<p> -<b>x < 1</b> ; <b>1 < x²</b> ⇔ <b>x < 1</b> ; <b>1 < x</b> <i>We square root both sides</i><br /> -</p> - - -<p> -We end up with a contradiction, therefor its wrong<br /> -</p> - - -<ol class="org-ol"> -<li>∀x ∈ ℝ, ∃y ∈ ℝ tels que y = 3x - 8<br /></li> -</ol> - - -<p> -I dont really understand this one, so let me translate it “For any value of x from the set of Real numbers, 3x - 8 is a Real number”…. i mean….yeah, we are substracting a Real number from an other real number…<br /> -</p> - -<p> -<b>Since substraction is an Internal composition law in ℝ, therefor all results of a substraction between two Real numbers is…Real</b><br /> -</p> - -<ol class="org-ol"> -<li><p> -∃x ∈ ℕ, ∀y ∈ ℕ, x > y ⇒ x + y < 8<br /> -</p> - -<p> -“There exists a number x from the set of Natural numbers such as for all values of y from the set of Natural numbers, x > y implies x + y < 8”<br /> -</p></li> -</ol> - - -<p> -Let’s get rid of the implication :<br /> -</p> - -<p> -∃x ∈ ℕ, ∀y ∈ ℕ, (y > x) ∨ (x + y < 8) <i>There exists a number x from the set of Natural numbers such as for all values of y from the set of Natural numbers y > x OR x + y < 8</i><br /> -</p> - -<p> -This proposition is true, because there exists a value of x that satisfies this condition, it’s <b>all numbers under 8</b> let’s take 3 as an example:<br /> -</p> - - -<p> -<b>x = 3 , if y > 3 then the first condition is true ; if y < 3 then the second one is true</b><br /> -</p> - - -<p> -Meaning that the two propositions CAN NOT BE WRONG TOGETHER, either one is wrong, or the other<br /> -</p> - - -<p> -y > x<br /> -</p> - - -<p> -<b>y - x > 0</b><br /> -</p> - - -<p> -y + x < 8<br /> -</p> - - -<p> -<b>y < 8 - x</b> <i>This one is always true for all values of x below 8, since we are working in the set ℕ</i><br /> -</p> - - -<ol class="org-ol"> -<li><p> -∀x ∈ ℝ, x² ≥ 1 ⇔ x ≥ 1<br /> -</p> - -<p> -….This is getting stupid. of course it’s true it’s part of the definition of the power of 2<br /> -</p></li> -</ol> -</div> -</li> -</ul> -</div> -</div> -</div> -<div id="outline-container-org21d6c03" class="outline-2"> -<h2 id="org21d6c03">2éme cours <i>Oct 2</i></h2> -<div class="outline-text-2" id="text-org21d6c03"> -</div> -<div id="outline-container-orgd6c9f49" class="outline-3"> -<h3 id="orgd6c9f49">Quantifiers</h3> -<div class="outline-text-3" id="text-orgd6c9f49"> -<p> -A propriety P can depend on a parameter x<br /> -</p> - - -<p> -∀ is the universal quantifier which stands for “For any value of…”<br /> -</p> - - -<p> -∃ is the existential quantifier which stands for “There exists at least one…”<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orge92d880"></a>Example<br /> -<div class="outline-text-6" id="text-orge92d880"> -<p> -P(x) : x+1≥0<br /> -</p> - -<p> -P(X) is True or False depending on the values of x<br /> -</p> -</div> -</li> -</ul> -<div id="outline-container-orgb332b43" class="outline-4"> -<h4 id="orgb332b43">Proprieties</h4> -<div class="outline-text-4" id="text-orgb332b43"> -</div> -<ul class="org-ul"> -<li><a id="org8587885"></a>Propriety Number 1:<br /> -<div class="outline-text-5" id="text-org8587885"> -<p> -The negation of the universal quantifier is the existential quantifier, and vice-versa :<br /> -</p> - -<ul class="org-ul"> -<li>not(∀x ∈ E , P(x)) ⇔ ∃ x ∈ E, not(P(x))<br /></li> -<li>not(∃x ∈ E , P(x)) ⇔ ∀ x ∈ E, not(P(x))<br /></li> -</ul> -</div> -<ul class="org-ul"> -<li><a id="org3a19f5f"></a>Example:<br /> -<div class="outline-text-6" id="text-org3a19f5f"> -<p> -∀ x ≥ 1 x² > 5 ⇔ ∃ x ≥ 1 x² < 5<br /> -</p> -</div> -</li> -</ul> -</li> -<li><a id="orgab7b647"></a>Propriety Number 2:<br /> -<div class="outline-text-5" id="text-orgab7b647"> -<p> -<b>∀x ∈ E, [P(x) ∧ Q(x)] ⇔ [∀ x ∈ E, P(x)] ∧ [∀ x ∈ E, Q(x)]</b><br /> -</p> - - -<p> -The propriety “For any value of x from a set E , P(x) and Q(x)” is equivalent to “For any value of x from a set E, P(x) AND for any value of x from a set E, Q(x)”<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org8ba49ff"></a>Example :<br /> -<div class="outline-text-6" id="text-org8ba49ff"> -<p> -P(x) : sqrt(x) > 0 ; Q(x) : x ≥ 1<br /> -</p> - - -<p> -∀x ∈ ℝ*+, [sqrt(x) > 0 , x ≥ 1] ⇔ [∀x ∈ R*+, sqrt(x) > 0] ∧ [∀x ∈ R*+, x ≥ 1]<br /> -</p> - - -<p> -<b>Which is true</b><br /> -</p> -</div> -</li> -</ul> -</li> -<li><a id="org91796f9"></a>Propriety Number 3:<br /> -<div class="outline-text-5" id="text-org91796f9"> -<p> -<b>∃ x ∈ E, [P(x) ∧ Q(x)] <i>⇒</i> [∃ x ∈ E, P(x)] ∧ [∃ x ∈ E, Q(x)]</b><br /> -</p> - - -<p> -<i>Here its an implication and not an equivalence</i><br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org1f20a27"></a>Example of why it’s NOT an equivalence :<br /> -<div class="outline-text-6" id="text-org1f20a27"> -<p> -P(x) : x > 5 ; Q(x) : x < 5<br /> -</p> - - -<p> -Of course there is no value of x such as its inferior and superior to 5 at the same time, so obviously the proposition is false. However, the two propositions separated are correct on their own, because there is a value of x such as its superior to 5, and there is also a value of x such as its inferior to 5. This is why it’s an implication and NOT AN EQUIVALENCE!!!<br /> -</p> -</div> -</li> -</ul> -</li> -<li><a id="org2b9f54b"></a>Propriety Number 4:<br /> -<div class="outline-text-5" id="text-org2b9f54b"> -<p> -<b>[∀ x ∈ E, P(x)] ∨ [∀ x ∈ E, Q(x)] <i>⇒</i> ∀x ∈ E, [P(x) ∨ Q(x)]</b><br /> -</p> - - -<p> -<i>Same here, implication and NOT en equivalence</i><br /> -</p> -</div> -</li> -</ul> -</div> -</div> -<div id="outline-container-orged685c1" class="outline-3"> -<h3 id="orged685c1">Multi-parameter proprieties :</h3> -<div class="outline-text-3" id="text-orged685c1"> -<p> -A propriety P can depend on two or more parameters, for convenience we call them x,y,z…etc<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org747b217"></a>Example :<br /> -<div class="outline-text-6" id="text-org747b217"> -<p> -P(x,y): x+y > 0<br /> -</p> - - -<p> -P(0,1) is a True proposition<br /> -</p> - - -<p> -P(-2,-1) is a False one<br /> -</p> -</div> -</li> -<li><a id="org5d93eaf"></a>WARNING :<br /> -<div class="outline-text-6" id="text-org5d93eaf"> -<p> -∀x ∈ E, ∃y ∈ F , P(x,y)<br /> -</p> - - -<p> -∃y ∈ F, ∀x ∈ E , P(x,y)<br /> -</p> - - -<p> -Are different because in the first one y depends on x, while in the second one, it doesn’t<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orgc60c61d"></a>Example :<br /> -<div class="outline-text-7" id="text-orgc60c61d"> -<p> -∀ x ∈ ℕ , ∃ y ∈ ℕ y > x -–— True<br /> -</p> - - -<p> -∃ y ∈ ℕ , ∀ x ∈ ℕ y > x -–— False<br /> -</p> -</div> -</li> -</ul> -</li> -</ul> -<li><a id="orgda9f614"></a>Proprieties :<br /> -<div class="outline-text-5" id="text-orgda9f614"> -<ol class="org-ol"> -<li>not(∀x ∈ E ,∃y ∈ F P(x,y)) ⇔ ∃x ∈ E, ∀y ∈ F not(P(x,y))<br /></li> -<li>not(∃x ∈ E ,∀y ∈ F P(x,y)) ⇔ ∀x ∈ E, ∃y ∈ F not(P(x,y))<br /></li> -</ol> -</div> -</li> -</ul> -</div> -<div id="outline-container-org78d7ed0" class="outline-3"> -<h3 id="org78d7ed0">Methods of mathematical reasoning :</h3> -<div class="outline-text-3" id="text-org78d7ed0"> -</div> -<div id="outline-container-org7d21c38" class="outline-4"> -<h4 id="org7d21c38">Direct reasoning :</h4> -<div class="outline-text-4" id="text-org7d21c38"> -<p> -To show that an implication P ⇒ Q is true, we suppose that P is true and we show that Q is true<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org59d34b3"></a>Example:<br /> -<div class="outline-text-5" id="text-org59d34b3"> -<p> -Let a,b be two Real numbers, we have to prove that <b>a² + b² = 1 ⇒ |a + b| ≤ 2</b><br /> -</p> - - -<p> -We suppose that a²+b² = 1 and we prove that |a + b| ≤ 2<br /> -</p> - - -<p> -a²+b²=1 ⇒ b² = 1 - a² ; a² = 1 - b²<br /> -</p> - - -<p> -a²+b²=1 ⇒ 1 - a² ≥ 0 ; 1 - b² ≥ 0<br /> -</p> - - -<p> -a²+b²=1 ⇒ a² ≤ 1 ; b² ≤ 1<br /> -</p> - - -<p> -a²+b²=1 ⇒ -1 ≤ a ≤ 1 ; -1 ≤ b ≤ 1<br /> -</p> - - -<p> -a²+b²=1 ⇒ -2 ≤ a + b ≤ 2<br /> -</p> - - -<p> -a²+b²=1 ⇒ |a + b| ≤ 2 <b>Which is what we wanted to prove, therefor the implication is correct</b><br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-orgcfd8723" class="outline-4"> -<h4 id="orgcfd8723">Reasoning by the Absurd:</h4> -<div class="outline-text-4" id="text-orgcfd8723"> -<p> -To prove that a proposition is True, we suppose that it’s False and we must come to a contradiction<br /> -</p> - - -<p> -And to prove that an implication P ⇒ Q is true using the reasoning by the absurd, we suppose that P ∧ not(Q) is true, and then we come to a contradiction as well<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orga4a0e2d"></a>Example:<br /> -<div class="outline-text-5" id="text-orga4a0e2d"> -<p> -Prove that this proposition is correct using the reasoning by the absurd : ∀x ∈ ℝ* , sqrt(1+x²) ≠ 1 + x²/2<br /> -</p> - - -<p> -We assume that ∃ x ℝ* , sqrt(1+x²) = 1 + x²/2<br /> -</p> - - -<p> -sqrt(1+x²) = 1 + x²/2 ; 1 + x² = (1+x²/2)² ; 1 + x² = 1 + x^4/4 + x² ; x^(4)/4 = 0 … Which contradicts with our proposition, since x = 4 and we are working on the ℝ* set<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org102d3fa" class="outline-4"> -<h4 id="org102d3fa">Reasoning by contraposition:</h4> -<div class="outline-text-4" id="text-org102d3fa"> -<p> -If an implication P ⇒ Q is too hard to prove, we just have to prove not(Q) ⇒ not(P) is true !!! or in other words that both not(P) and not(Q) are true<br /> -</p> -</div> -</div> -<div id="outline-container-org81cb388" class="outline-4"> -<h4 id="org81cb388">Reasoning by counter example:</h4> -<div class="outline-text-4" id="text-org81cb388"> -<p> -To prove that a proposition ∀x ∈ E, P(x) is false, all we have to do is find a single value of x from E such as not(P(x)) is true<br /> -</p> -</div> -</div> -</div> -</div> -<div id="outline-container-orgc2178b8" class="outline-2"> -<h2 id="orgc2178b8">3eme Cours : <i>Oct 9</i></h2> -<div class="outline-text-2" id="text-orgc2178b8"> -</div> -<div id="outline-container-org4855f6f" class="outline-4"> -<h4 id="org4855f6f">Reasoning by recurrence :</h4> -<div class="outline-text-4" id="text-org4855f6f"> -<p> -P is a propriety dependent of <b>n ∈ ℕ</b>. If for n0 ∈ ℕ P(n0) is true, and if for n ≥ n0 (P(n) ⇒ P(n+1)) is true. Then P(n) is true for n ≥ n0<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orga792d9c"></a>Example:<br /> -<div class="outline-text-5" id="text-orga792d9c"> -<p> -Let’s prove that ∀ n ≥ 1 , (n,k=1)Σk = [n(n+1)]/2<br /> -</p> - - -<p> -P(n) : (n,k=1)Σk = [n(n+1)]/2<br /> -</p> - - - -<p> -<b>Pour n = 1:</b> (1,k=1)Σk = 1 ; [n(n+1)]/2 = 1 . <b>So P(1) is true</b><br /> -</p> - - - -<p> -For n ≥ 1. We assume that P(n) is true, OR : <b>(n, k=1)Σk = n(n+1)/2</b>. We now have to prove that P(n+1) is true, Or : <b>(n+1, k=1)Σk = (n+1)(n+2)/2</b><br /> -</p> - - -<p> -(n+1, k=1)Σk = 1 + 2 + …. + n + (n+1) ; (n+1, k=1)Σk = (n, k=1)Σk + (n+1) ; = n(n+1)/2 + (n+1) ; = [n(n+1) + 2(n+1)]/2 ; = <b>[(n+2)(n+1)]/2</b> <i>WHICH IS WHAT WE NEEDED TO FIND</i><br /> -</p> - - -<p> -<b>Conclusion: ∀n ≥ 1 , (n,k=1)Σk = n(n+1)/2</b><br /> -</p> -</div> -</li> -</ul> -</div> -</div> -<div id="outline-container-orgde6bfac" class="outline-2"> -<h2 id="orgde6bfac">4eme Cours : Chapitre 2 : Sets and Operations</h2> -<div class="outline-text-2" id="text-orgde6bfac"> -</div> -<div id="outline-container-orgfe8000a" class="outline-3"> -<h3 id="orgfe8000a">Definition of a set :</h3> -<div class="outline-text-3" id="text-orgfe8000a"> -<p> -A set is a collection of objects that share the sane propriety<br /> -</p> -</div> -</div> -<div id="outline-container-orgfe04671" class="outline-3"> -<h3 id="orgfe04671">Belonging, inclusion, and equality :</h3> -<div class="outline-text-3" id="text-orgfe04671"> -<ol class="org-ol"> -<li>Let E be a set. If x is an element of E, we say that x belongs to E we write <b>x ∈ E</b>, and if it doesn’t, we write <b>x ∉ E</b><br /></li> -<li>A set E is included in a set F if all elements of E are elements of F and we write <b>E ⊂ F ⇔ (∀x , x ∈ E ⇒ x ∈ F)</b>. We say that E is a subset of F, or a part of F. The negation of this propriety is : <b>E ⊄ F ⇔ ∃x , x ∈ E and x ⊄ F</b><br /></li> -<li>E and F are equal if E is included in F and F is included in E, and we write <b>E = F ⇔ (E ⊂ F) et (F ⊂ E)</b><br /></li> -<li>The empty set (symbolized by ∅) is a set without elements, and is included in all sets (by convention) : <b>∅ ⊂ E</b><br /></li> -</ol> -</div> -</div> -<div id="outline-container-orga2eb99d" class="outline-3"> -<h3 id="orga2eb99d">Intersections and reunions :</h3> -<div class="outline-text-3" id="text-orga2eb99d"> -</div> -<div id="outline-container-org560d563" class="outline-4"> -<h4 id="org560d563">Intersection:</h4> -<div class="outline-text-4" id="text-org560d563"> -<p> -E ∩ F = {x / x ∈ E AND x ∈ F} ; x ∈ E ∩ F ⇔ x ∈ F AND x ∈ F<br /> -</p> - - -<p> -x ∉ E ∩ F ⇔ x ∉ E OR x ∉ F<br /> -</p> -</div> -</div> -<div id="outline-container-org7147bc3" class="outline-4"> -<h4 id="org7147bc3">Union:</h4> -<div class="outline-text-4" id="text-org7147bc3"> -<p> -E ∪ F = {x / x ∈ E OR x ∈ F} ; x ∈ E ∪ F ⇔ x ∈ F OR x ∈ F<br /> -</p> - - -<p> -x ∉ E ∪ F ⇔ x ∉ E AND x ∉ F<br /> -</p> -</div> -</div> -<div id="outline-container-org16b5ab2" class="outline-4"> -<h4 id="org16b5ab2">Difference between two sets:</h4> -<div class="outline-text-4" id="text-org16b5ab2"> -<p> -E(Which is also written as : E - F) = {x / x ∈ E and x ∉ F}<br /> -</p> -</div> -</div> -<div id="outline-container-orgdac190b" class="outline-4"> -<h4 id="orgdac190b">Complimentary set:</h4> -<div class="outline-text-4" id="text-orgdac190b"> -<p> -If F ⊂ E. E - F is the complimentary of F in E.<br /> -</p> - - -<p> -FCE = {x /x ∈ E AND x ∉ F} <b>ONLY WHEN F IS A SUBSET OF E</b><br /> -</p> -</div> -</div> -<div id="outline-container-org4e0b111" class="outline-4"> -<h4 id="org4e0b111">Symmetrical difference</h4> -<div class="outline-text-4" id="text-org4e0b111"> -<p> -E Δ F = (E - F) ∪ (F - E) ; = (E ∪ F) - (E ∩ F)<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org691c863" class="outline-3"> -<h3 id="org691c863">Proprieties :</h3> -<div class="outline-text-3" id="text-org691c863"> -<p> -Let E,F and G be 3 sets. We have :<br /> -</p> -</div> -<div id="outline-container-org9cc9f31" class="outline-4"> -<h4 id="org9cc9f31">Commutativity:</h4> -<div class="outline-text-4" id="text-org9cc9f31"> -<p> -E ∩ F = F ∩ E<br /> -E ∪ F = F ∪ E<br /> -</p> -</div> -</div> -<div id="outline-container-org471083b" class="outline-4"> -<h4 id="org471083b">Associativity:</h4> -<div class="outline-text-4" id="text-org471083b"> -<p> -E ∩ (F ∩ G) = (E ∩ F) ∩ G<br /> -E ∪ (F ∪ G) = (E ∪ F) ∪ G<br /> -</p> -</div> -</div> -<div id="outline-container-orge63be10" class="outline-4"> -<h4 id="orge63be10">Distributivity:</h4> -<div class="outline-text-4" id="text-orge63be10"> -<p> -E ∩ (F ∪ G) = (E ∩ F) ∪ (E ∩ G)<br /> -E ∪ (F ∩ G) = (E ∪ F) ∩ (E ∪ G)<br /> -</p> -</div> -</div> -<div id="outline-container-orgfb01947" class="outline-4"> -<h4 id="orgfb01947">Lois de Morgan:</h4> -<div class="outline-text-4" id="text-orgfb01947"> -<p> -If E ⊂ G and F ⊂ G ;<br /> -</p> - -<p> -(E ∩ F)CG = ECG ∪ FCG ; (E ∪ F)CG = ECG ∩ FCG<br /> -</p> -</div> -</div> -<div id="outline-container-orge1a41eb" class="outline-4"> -<h4 id="orge1a41eb">An other one:</h4> -<div class="outline-text-4" id="text-orge1a41eb"> -<p> -E - (F ∩ G) = (E-F) ∪ (E-G) ; E - (F ∪ G) = (E-F) ∩ (E-G)<br /> -</p> -</div> -</div> -<div id="outline-container-org9939b0f" class="outline-4"> -<h4 id="org9939b0f">An other one:</h4> -<div class="outline-text-4" id="text-org9939b0f"> -<p> -E ∩ ∅ = ∅ ; E ∪ ∅ = E<br /> -</p> -</div> -</div> -<div id="outline-container-org90bfdc4" class="outline-4"> -<h4 id="org90bfdc4">And an other one:</h4> -<div class="outline-text-4" id="text-org90bfdc4"> -<p> -E ∩ (F Δ G) = (E ∩ F) Δ (E ∩ G)<br /> -</p> -</div> -</div> -<div id="outline-container-org1e49001" class="outline-4"> -<h4 id="org1e49001">And the last one:</h4> -<div class="outline-text-4" id="text-org1e49001"> -<p> -E Δ ∅ = E ; E Δ E = ∅<br /> -</p> -</div> -</div> -</div> -</div> -<div id="outline-container-org272eca3" class="outline-2"> -<h2 id="org272eca3">5eme cours: L’ensemble des parties d’un ensemble <i>Oct 16</i></h2> -<div class="outline-text-2" id="text-org272eca3"> -<p> -Let E be a set. We define P(E) as the set of all parts of E : <b>P(E) = {X/X ⊂ E}</b><br /> -</p> -</div> -<div id="outline-container-org5b29e32" class="outline-4"> -<h4 id="org5b29e32">Notes :</h4> -<div class="outline-text-4" id="text-org5b29e32"> -<p> -∅ ∈ P(E) ; E ∈ P(E)<br /> -</p> - - -<p> -cardinal E = n <i>The number of terms in E</i> , cardinal P(E) = 2^n <i>The number of all parts of E</i><br /> -</p> -</div> -</div> -<div id="outline-container-org5636bd8" class="outline-4"> -<h4 id="org5636bd8">Examples :</h4> -<div class="outline-text-4" id="text-org5636bd8"> -<p> -E = {a,b,c} ; P(E)={∅, {a}, {b}, {c}, {a,b}, {b,c}, {a,c}, {a,b,c}}<br /> -</p> -</div> -</div> -<div id="outline-container-orgd8cb2c3" class="outline-3"> -<h3 id="orgd8cb2c3">Partition of a set :</h3> -<div class="outline-text-3" id="text-orgd8cb2c3"> -<p> -We say that <b>A</b> is a partition of E if:<br /> -</p> -<ol class="org-ol"> -<li>∀ x ∈ A , x ≠ 0<br /></li> -<li>All the elements of <b>A</b> are two by two disjoint. Or in other terms, there should not be two elements that intersects with each other.<br /></li> -<li>The reunion of all elements of <b>A</b> is equal to E<br /></li> -</ol> -</div> -</div> -<div id="outline-container-orgf40404d" class="outline-3"> -<h3 id="orgf40404d">Cartesian products :</h3> -<div class="outline-text-3" id="text-orgf40404d"> -<p> -Let E and F be two sets, the set EXF = {(x,y)/ x ∈ E AND y ∈ F} is called the Cartesian product of E and F<br /> -</p> -</div> -<div id="outline-container-orgd526cb8" class="outline-4"> -<h4 id="orgd526cb8">Example :</h4> -<div class="outline-text-4" id="text-orgd526cb8"> -<p> -A = {4,5} ; B= {4,5,6} ; AxB = {(4,4), (4,5), (4,6), (5,4), (5,5), (5,6)}<br /> -</p> - - -<p> -BxA = {(4,4), (4,5), (5,4), (5,5), (6,4), (6,5)} ; Therefore AxB ≠ BxA<br /> -</p> -</div> -</div> -<div id="outline-container-org56dd088" class="outline-4"> -<h4 id="org56dd088">Some proprieties:</h4> -<div class="outline-text-4" id="text-org56dd088"> -<ol class="org-ol"> -<li>ExF = ∅ ⇔ E=∅ OR F=∅<br /></li> -<li>ExF = FxE ⇔ E=F OR E=∅ OR F=∅<br /></li> -<li>E x (F∪G) = (ExF) ∪ (ExG)<br /></li> -<li>(E∪F) x G = (ExG) ∪ (FxG)<br /></li> -<li>(E∪F) ∩ (GxH) = (E ∩ G) x (F ∩ H)<br /></li> -<li>Generally speaking : (ExF) ∪ (GxH) ≠ (E∪G) x (F∪H)<br /></li> -</ol> -</div> -</div> -</div> -</div> -<div id="outline-container-org5ee4278" class="outline-2"> -<h2 id="org5ee4278">Binary relations in a set :</h2> -<div class="outline-text-2" id="text-org5ee4278"> -</div> -<div id="outline-container-orgddc9af6" class="outline-3"> -<h3 id="orgddc9af6">Definition :</h3> -<div class="outline-text-3" id="text-orgddc9af6"> -<p> -Let E be a set and x,y ∈ E. If there exists a link between x and y, we say that they are tied by a relation <b>R</b> and we write <b>xRy</b><br /> -</p> -</div> -</div> -<div id="outline-container-orge65424e" class="outline-3"> -<h3 id="orge65424e">Proprieties :</h3> -<div class="outline-text-3" id="text-orge65424e"> -<p> -Let E be a set and R a relation defined in E<br /> -</p> -<ol class="org-ol"> -<li>We say that R is reflexive if ∀ x ∈ E, xRx (for any element x in E,x is related to itself)<br /></li> -<li>We say that R is symmetrical if ∀ x,y ∈ E , xRy ⇒ yRx<br /></li> -<li>We say that R is transitive if ∀ x,y,z ∈ E (xRy , yRz) ⇒ xRz<br /></li> -<li>We say that R is anti-symmetrical if ∀ x,y ∈ E xRy AND yRx ⇒ x = y<br /></li> -</ol> -</div> -</div> -<div id="outline-container-orgd7877d3" class="outline-3"> -<h3 id="orgd7877d3">Equivalence relationship :</h3> -<div class="outline-text-3" id="text-orgd7877d3"> -<p> -We say that R is a relation of equivalence in E if its reflexive, symetrical and transitive<br /> -</p> -</div> -<div id="outline-container-org85cf025" class="outline-4"> -<h4 id="org85cf025">Equivalence class :</h4> -<div class="outline-text-4" id="text-org85cf025"> -<p> -Let R be a relation of equivalence in E and a ∈ E, we call equivalence class of <b>a</b>, and we write ̅a or ȧ, or cl a the following set :<br /> -</p> - - -<p> -<b>a̅ = {y ∈ E/ y R a}</b><br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orga316a01"></a>The quotient set :<br /> -<div class="outline-text-5" id="text-orga316a01"> -<p> -E/R = {̅a , a ∈ E}<br /> -</p> -</div> -</li> -</ul> -</div> -</div> -<div id="outline-container-orge18dcc7" class="outline-3"> -<h3 id="orge18dcc7">Order relationship :</h3> -<div class="outline-text-3" id="text-orge18dcc7"> -<p> -Let E be a set and R be a relation defined in E. We say that R is a relation of order if its reflexive, anti-symetrical and transitive.<br /> -</p> -<ol class="org-ol"> -<li>The order R is called total if ∀ x,y ∈ E xRy OR yRx<br /></li> -<li>The order R is called partial if ∃ x,y ∈ E xR̅y AND yR̅x<br /></li> -</ol> -</div> -<div id="outline-container-org60d471a" class="outline-4"> -<h4 id="org60d471a"><span class="todo TODO">TODO</span> Examples :</h4> -<div class="outline-text-4" id="text-org60d471a"> -<p> -∀x,y ∈ ℝ , xRy ⇔ x²-y²=x-y<br /> -</p> -<ol class="org-ol"> -<li>Prove that R is an equivalence relation<br /></li> -<li>Let a ∈ ℝ, find ̅a<br /></li> -</ol> -</div> -</div> -</div> -</div> -<div id="outline-container-org77de6e3" class="outline-2"> -<h2 id="org77de6e3">TP exercices <i>Oct 20</i> :</h2> -<div class="outline-text-2" id="text-org77de6e3"> -</div> -<div id="outline-container-org3ca8006" class="outline-3"> -<h3 id="org3ca8006">Exercice 3 :</h3> -<div class="outline-text-3" id="text-org3ca8006"> -</div> -<div id="outline-container-orgad95ec3" class="outline-4"> -<h4 id="orgad95ec3">Question 3</h4> -<div class="outline-text-4" id="text-orgad95ec3"> -<p> -Montrer par l’absurde que P : ∀x ∈ ℝ*, √(4+x³) ≠ 2 + x³/4 est vraies<br /> -</p> - -<p class="verse"> -On suppose que ∃ x ∈ ℝ* , √(4+x³) = 2 + x³/4<br /> -4+x³ = (2 + x³/4)²<br /> -4+x³ = 4 + x⁶/16 + 4*(x³/4)<br /> -4+x³ = 4 + x⁶/16 + x³<br /> -x⁶/16 = 0<br /> -x⁶ = 0<br /> -x = 0 . Or, x appartiens a ℝ\{0}, donc P̅ est fausse. Ce qui est equivalent a dire que P est vraie<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org8180ae0" class="outline-3"> -<h3 id="org8180ae0">Exercice 4 :</h3> -<div class="outline-text-3" id="text-org8180ae0"> -</div> -<div id="outline-container-orgfe0b1e2" class="outline-4"> -<h4 id="orgfe0b1e2"><span class="done DONE">DONE</span> Question 1 :</h4> -<div class="outline-text-4" id="text-orgfe0b1e2"> -<p class="verse"> -∀ n ∈ ℕ* , (n ,k=1)Σ1/k(k+1) = 1 - 1/1+n<br /> -P(n) : (n ,k=1)Σ1/k(k+1) = 1 - 1/1+n<br /> -1. <b>On vérifie P(n) pour n = 1</b><br /> -(1 ,k=1)Σ1/k(k+1) = 1/1(1+1)<br /> -                  = 1/2 — (1)<br /> -1 - 1/1+1 = 1 - 1/2<br /> -                  = 1/2 — (2)<br /> -De (1) et (2), P(0) est vraie -— (a)<br /> -<br /> -2. <b>On suppose que P(n) est vraie pour n ≥ n1 puis on vérifie pour n+1</b><br /> -(n ,k=1)Σ1/k(k+1) = 1 - 1/1+n<br /> -(n ,k=1)Σ1/k(k+1) + 1/(n+1)(n+2) = 1 - (1/(1+n)) + 1/(n+1)(n+2)<br /> -(n+1 ,k=1)Σ1/k(k+1) = 1 - 1/(n+1) + 1/[(n+1)(n+2)]<br /> -(n+1 ,k=1)Σ1/k(k+1) = 1 + 1/[(n+1)(n+2)] - (n+2)/[(n+1)(n+2)]<br /> -(n+1 ,k=1)Σ1/k(k+1) = 1 + [1-(n+2)]/[(n+1)(n+2)]<br /> -(n+1 ,k=1)Σ1/k(k+1) = 1 + [-n-1]/[(n+1)(n+2)]<br /> -(n+1 ,k=1)Σ1/k(k+1) = 1 - [n+1]/[(n+1)(n+2)]<br /> -(n+1 ,k=1)Σ1/k(k+1) = 1 - 1/(n+1+1) <b>CQFD</b><br /> -<br /> -Donc P(n+1) est vraie. -— (b)<br /> -De (a) et (b) on conclus que la proposition de départ est vraie<br /> -</p> -</div> -</div> -</div> -</div> -<div id="outline-container-org2d6e0ba" class="outline-2"> -<h2 id="org2d6e0ba">Chapter 3 : Applications</h2> -<div class="outline-text-2" id="text-org2d6e0ba"> -</div> -<div id="outline-container-orga5be12f" class="outline-3"> -<h3 id="orga5be12f">3.1 Generalities about applications :</h3> -<div class="outline-text-3" id="text-orga5be12f"> -</div> -<div id="outline-container-org805d7bc" class="outline-4"> -<h4 id="org805d7bc">Definition :</h4> -<div class="outline-text-4" id="text-org805d7bc"> -<p> -Let E and F be two sets.<br /> -</p> -<ol class="org-ol"> -<li>We call a function of the set E to the set F any relation from E to F such as for any element of E, we can find <span class="underline">at most one</span> element of F that corresponds to it.<br /></li> -<li>We call an application of the set E to the set F a relation from E to F such as for any element of E, we can find <span class="underline">one and only one</span> element of F that corresponds to it.<br /></li> -<li><p> -f: E<sub>1</sub> —> F<sub>1</sub> ; g: E<sub>2</sub> —> F<sub>2</sub> ; f ≡ g ⇔ [E<sub>1 </sub>= E<sub>2</sub> ; F<sub>1</sub> = F<sub>2</sub> ; f(x) = g(x) ∀x ∈ E<sub>1</sub><br /> -</p> - -<p> -Generally speaking, we schematize a function or an application by this writing :<br /> -</p> -<p class="verse"> -f : E —> F<br /> -    x —> f(x)=y<br /> -   Γ = {(x , f(x))/ x ∈ E ; f(x) ∈ F} is the graph of f<br /> -</p></li> -</ol> -</div> -<ul class="org-ul"> -<li><a id="org2936c19"></a>Some examples :<br /> -<ul class="org-ul"> -<li><a id="orgd77c836"></a>Ex1:<br /> -<div class="outline-text-6" id="text-orgd77c836"> -<p class="verse"> -f : ℝ —> ℝ<br /> -    x —> f(x) = (x-1)/x<br /> -is a function, because 0 does NOT have a corresponding element using that relation.<br /> -</p> -</div> -</li> -<li><a id="orga45fd32"></a>Ex2:<br /> -<div class="outline-text-6" id="text-orga45fd32"> -<p class="verse"> -f : ℝ<sup>*</sup> —> ℝ<br /> -    x —> f(x)= (x-1)/x<br /> -is, however, an application<br /> -</p> -</div> -</li> -</ul> -</li> -</ul> -</div> -<div id="outline-container-org7947331" class="outline-4"> -<h4 id="org7947331">Restriction and prolongation of an application :</h4> -<div class="outline-text-4" id="text-org7947331"> -<p> -Let f : E -> F an application and E<sub>1</sub> ⊂ E therefore :<br /> -</p> -<p class="verse"> -g : E<sub>1</sub> -> F<br /> -g(x) = f(x) ∀x ∈ E<sub>1</sub><br /> -<br /> -g is called the <b>restriction</b> of f to E<sub>1</sub>. And f is called the <b>prolongation</b> of g to E.<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org7c848c6"></a>Example<br /> -<div class="outline-text-5" id="text-org7c848c6"> -<p class="verse"> -f : ℝ —> ℝ<br /> -    x —> f(x) = x<sup>2</sup><br /> -<br /> -g : [0 , <del>∞[ —> ℝ<br /> -    x —> g(x) = x²<br /> -<br /> -g is called the <b>restriction</b> of f to ℝ^{</del>}. And f is called the <b>prolongation</b> of g to ℝ.<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-orgd94bc69" class="outline-4"> -<h4 id="orgd94bc69">Composition of applications :</h4> -<div class="outline-text-4" id="text-orgd94bc69"> -<p> -Let E,F, and G be three sets, f: E -> F and g: F -> G are two applications. We define their composition, symbolized by g<sub>o</sub>f as follow :<br /> -</p> - - -<p> -g<sub>o</sub>f : E -> G . ∀x ∈ E (g<sub>o</sub>f)<sub>(x)</sub>= g(f(x))<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org257d05a" class="outline-3"> -<h3 id="org257d05a">3.2 Injection, surjection and bijection :</h3> -<div class="outline-text-3" id="text-org257d05a"> -<p> -Let f: E -> F be an application :<br /> -</p> -<ol class="org-ol"> -<li>We say that f is injective if : ∀x,x’ ∈ E : f(x) = f(x’) ⇒ x = x’<br /></li> -<li>We say that f is surjective if : ∀ y ∈ F , ∃ x ∈ E : y = f(x)<br /></li> -<li>We say that if is bijective if it’s both injective and surjective at the same time.<br /></li> -</ol> -</div> -<div id="outline-container-org1612e09" class="outline-4"> -<h4 id="org1612e09">Proposition :</h4> -<div class="outline-text-4" id="text-org1612e09"> -<p> -Let f : E -> F be an application. Therefore:<br /> -</p> -<ol class="org-ol"> -<li>f is injective ⇔ y = f(x) has at most one solution.<br /></li> -<li>f is surjective ⇔ y = f(x) has at least one solution.<br /></li> -<li>f is bijective ⇔ y = f(x) has a single and unique solution.<br /></li> -</ol> -</div> -</div> -</div> -<div id="outline-container-orgebdf518" class="outline-3"> -<h3 id="orgebdf518">3.3 Reciprocal applications :</h3> -<div class="outline-text-3" id="text-orgebdf518"> -</div> -<div id="outline-container-orgf072e42" class="outline-4"> -<h4 id="orgf072e42">Def :</h4> -<div class="outline-text-4" id="text-orgf072e42"> -<p> -Let f : E -> F a bijective application. So there exists an application named f<sup>-1</sup> : F -> E such as : y = f(x) ⇔ x = f<sup>-1</sup>(y)<br /> -</p> -</div> -</div> -<div id="outline-container-org244b352" class="outline-4"> -<h4 id="org244b352">Theorem :</h4> -<div class="outline-text-4" id="text-org244b352"> -<p> -Let f : E -> F be a bijective application. Therefore its reciprocal f<sup>-1</sup> verifies : f<sup>-1</sup><sub>o</sub>f=Id<sub>E </sub>; f<sub>o</sub>f<sup>-1</sup>=Id<sub>F</sub> Or :<br /> -</p> - - -<p> -Id<sub>E</sub> : E -> E ; x -> Id<sub>E</sub>(x) = x<br /> -</p> -</div> -</div> -<div id="outline-container-org1479c0e" class="outline-4"> -<h4 id="org1479c0e">Some proprieties :</h4> -<div class="outline-text-4" id="text-org1479c0e"> -<ol class="org-ol"> -<li>(f<sup>-1</sup>)<sup>-1</sup> = f<br /></li> -<li>(g<sub>o</sub>f)⁻¹ = f⁻¹<sub>o</sub>g⁻¹<br /></li> -<li>The graphs of f and f⁻¹ are symmetrical to each other by the first bis-sectrice of the equation y = x<br /></li> -</ol> -</div> -</div> -</div> -<div id="outline-container-orgaf81bb3" class="outline-3"> -<h3 id="orgaf81bb3">3.4 Direct Image and reciprocal Image :</h3> -<div class="outline-text-3" id="text-orgaf81bb3"> -</div> -<div id="outline-container-org87b91e2" class="outline-4"> -<h4 id="org87b91e2">Direct Image :</h4> -<div class="outline-text-4" id="text-org87b91e2"> -<p> -Let f: E-> F be an application and A ⊂ E. We call a direct image of A by f, and we symbolize as f(A) the subset of F defined by :<br /> -</p> - - -<p> -f(A) = {f(x)/ x ∈ A} ; = { y ∈ F ∃ x ∈ A y=f(x)}<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orgb5bc08c"></a>Example :<br /> -<div class="outline-text-5" id="text-orgb5bc08c"> -<p class="verse"> -f: ℝ -> ℝ<br /> -   x -> f(x) = x²<br /> -A = {0,4}<br /> -f(A) = {f(0), f(4)} = {0, 16}<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org500bc40" class="outline-4"> -<h4 id="org500bc40">Reciprocal image :</h4> -<div class="outline-text-4" id="text-org500bc40"> -<p> -Let f: E -> F be an application and B ⊂ F. We call the reciprocal image of E by F the subset f<sup>-1</sup>(B) :<br /> -</p> - - -<p> -f<sup>-1</sup>(B) = {x ∈ E/f(x) ∈ B} ; x ∈ f<sup>-1</sup>(B) ⇔ f(x) ∈ B<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org885d21d"></a>Example :<br /> -<div class="outline-text-5" id="text-org885d21d"> -<p class="verse"> -f: ℝ -> ℝ<br /> -   x -> f(x) = x²<br /> -B = {1,9,4}<br /> -f<sup>-1</sup>(B) = {1,-1,2,-2,3,-3}<br /> -      = {x ∈ ℝ/x² ∈ {1,4,9}}<br /> -</p> -</div> -</li> -</ul> -</div> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2023-11-01 Wed 20:17</p> -</div> -</body> -</html> \ No newline at end of file diff --git a/uni_notes/alsd.html b/uni_notes/alsd.html deleted file mode 100755 index 804d386..0000000 --- a/uni_notes/alsd.html +++ /dev/null @@ -1,109 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" 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id="text-table-of-contents" role="doc-toc"> -<ul> -<li><a href="#org99d5220">Contenu de la Matiére</a> -<ul> -<li><a href="#orgbd002d7">Chapitre 1: Elements de Base</a></li> -<li><a href="#orgeb962fb">Chapitre 2: Présentation du formalisme Algorithmique</a></li> -<li><a href="#org7a1fb51">Chapitre 3: Eléments de base du language C</a></li> -<li><a href="#org5f789aa">Chapitre 4: Modularité( Fonction et Procédure )</a></li> -<li><a href="#org330830d">Chapitre 5: Les structures des données statiques</a></li> -</ul> -</li> -<li><a href="#orgced3d78">Premier cours : Algorithmes <i>Oct 1</i> :</a> -<ul> -<li><a href="#orga9ff303">Définition d’un algorithm :</a> -<ul> -<li><a href="#org38de9fd">Example d’un Algo : Résolution d’une équation du second ordre (ax²+bx+c=0)</a></li> -</ul> -</li> -</ul> -</li> -</ul> -</div> -</div> -<div id="outline-container-org99d5220" class="outline-2"> -<h2 id="org99d5220">Contenu de la Matiére</h2> -<div class="outline-text-2" id="text-org99d5220"> -</div> -<div id="outline-container-orgbd002d7" class="outline-3"> -<h3 id="orgbd002d7">Chapitre 1: Elements de Base</h3> -<div class="outline-text-3" id="text-orgbd002d7"> -<ul class="org-ul"> -<li>Algorithmique, procésseur, action.<br /></li> -<li>Programme et languages de programmation.<br /></li> -<li>Analyse des problémes.<br /></li> -</ul> -</div> -</div> -<div id="outline-container-orgeb962fb" class="outline-3"> -<h3 id="orgeb962fb">Chapitre 2: Présentation du formalisme Algorithmique</h3> -</div> -<div id="outline-container-org7a1fb51" class="outline-3"> -<h3 id="org7a1fb51">Chapitre 3: Eléments de base du language C</h3> -</div> -<div id="outline-container-org5f789aa" class="outline-3"> -<h3 id="org5f789aa">Chapitre 4: Modularité( Fonction et Procédure )</h3> -</div> -<div id="outline-container-org330830d" class="outline-3"> -<h3 id="org330830d">Chapitre 5: Les structures des données statiques</h3> -</div> -</div> -<div id="outline-container-orgced3d78" class="outline-2"> -<h2 id="orgced3d78">Premier cours : Algorithmes <i>Oct 1</i> :</h2> -<div class="outline-text-2" id="text-orgced3d78"> -</div> -<div id="outline-container-orga9ff303" class="outline-3"> -<h3 id="orga9ff303">Définition d’un algorithm :</h3> -<div class="outline-text-3" id="text-orga9ff303"> -<p> -Un ensemble d’opérations ecrites dans le language naturel.<br /> -</p> -</div> -<div id="outline-container-org38de9fd" class="outline-4"> -<h4 id="org38de9fd">Example d’un Algo : Résolution d’une équation du second ordre (ax²+bx+c=0)</h4> -<div class="outline-text-4" id="text-org38de9fd"> -<ol class="org-ol"> -<li>Si a=0 ET b=0 alors <b>l’équation n’est pas du 2nd ordre</b>.<br /></li> -<li>Si a=0 et b≠0 alors <b>x= -c/5</b> .<br /></li> -<li>Si a≠0 alors <b>calculer Δ= b²-4ac</b> :<br /> -<ol class="org-ol"> -<li>Si Δ=0 alors <b>x=-b/2a</b>.<br /></li> -<li>Si Δ<0 alors <b>l’équation n’as pas de solution</b>.<br /></li> -<li>Si Δ>0 alors <b>x=[-b±sqrt(Δ)]/2a</b><br /></li> -</ol></li> -</ol> -</div> -</div> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2023-11-01 Wed 20:17</p> -</div> -</body> -</html> \ No newline at end of file diff --git a/uni_notes/analyse.html b/uni_notes/analyse.html deleted file mode 100755 index 0c2f952..0000000 --- a/uni_notes/analyse.html +++ /dev/null @@ -1,1624 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2023-11-14 Tue 23:06 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>Analyse 1</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="https://crystal.tilde.institute/favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href="../../../uni_notes/"> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title">Analyse 1</h1> -<div id="table-of-contents" role="doc-toc"> -<h2>Table of Contents</h2> -<div id="text-table-of-contents" role="doc-toc"> -<ul> -<li><a href="#org51375f0">Contenu de la Matiére</a> -<ul> -<li><a href="#orgd074219">Chapitre 1 : Quelque propriétés de ℝ</a></li> -<li><a href="#orgb5220df">Chapitre 2 : Les suites numériques réelles</a></li> -<li><a href="#orge7b80f9">Chapitre 3 : Limites et continuité des fonctions réelles d’une variable réelle</a></li> -<li><a href="#orgcc6964b">Chapitre 4 : La dérivabilité et son interprétation géometrique</a></li> -<li><a href="#orgea870f0">Chapitre 5 : Les fonctions trigonométriques réciproques, fonctions hypérboliques réciproques</a></li> -</ul> -</li> -<li><a href="#org7dbe2a4">Premier cours : Quelque propriétés de ℝ <i>Sep 26</i> :</a> -<ul> -<li><a href="#org4b25f0c">La loi de composition interne dans E :</a> -<ul> -<li><a href="#orgc048164"><b>Example : Addition</b></a></li> -<li><a href="#orgadeeaa1"><b>Example : soustraction</b></a></li> -</ul> -</li> -<li><a href="#orge686f2a">La loi de composition externe dans E :</a></li> -<li><a href="#org96fc192">Groupes :</a> -<ul> -<li><a href="#org9cae959">Il contiens un élement neutre</a></li> -<li><a href="#orgfc1fc7b">Il contiens un élément symétrique</a></li> -<li><a href="#orge76674f">@ est cummutative :</a></li> -</ul> -</li> -<li><a href="#orgde40808">Anneaux :</a> -<ul> -<li><a href="#org6960733">(E ; @) est un groupe cummutatif</a></li> -<li><a href="#org3dd13c2">! est une loi associative :</a></li> -<li><a href="#org96e7790">Distribution de ! par rapport à @ :</a></li> -<li><a href="#orgaaceb67">L’existance d’un élèment neutre de ! :</a></li> -<li><a href="#org07575e5">! est cummutative :</a></li> -</ul> -</li> -<li><a href="#org4dde6a2">Corps :</a> -<ul> -<li><a href="#orga3ea966">La symétrie :</a></li> -</ul> -</li> -<li><a href="#org316172f">Exercice : (ℝ, +, x) corps ou pas ?</a> -<ul> -<li><a href="#org4ed9aef">Est-ce un Anneau ?</a></li> -<li><a href="#org248a5ea">Est-ce un corps ?</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#org0b3fce2">2nd cours :L’ordre dans ℝ, Majorant, minorant, borne superieure, borne inférieure <i>Oct 3</i> :</a> -<ul> -<li><a href="#orga3c4b3c">L’ordre dans ℝ</a> -<ul> -<li><a href="#org9b04907">Exemples :</a></li> -</ul> -</li> -<li><a href="#org824efff">Majorant, minorant, borne supérieure, borne inférieure</a> -<ul> -<li><a href="#org34c228b">Majorant:</a></li> -<li><a href="#orgc832fb0">Minorant:</a></li> -<li><a href="#org3cb02e2">Borne supérieure:</a></li> -<li><a href="#orgef4458e">Borne inférieure:</a></li> -<li><a href="#org2b2908f">Maximum :</a></li> -<li><a href="#org1410a06">Minimum :</a></li> -<li><a href="#orgd1fcd4e">Remarques :</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#orgc939931">3rd cours :Les suites numériques <i>Oct 5</i> :</a> -<ul> -<li> -<ul> -<li><a href="#org8607984">Définition :</a></li> -<li><a href="#orgcc2100f">Définition N°2 :</a></li> -</ul> -</li> -<li><a href="#org69f8c52">Opérations sur les suites :</a> -<ul> -<li><a href="#orgf01d039">La somme :</a></li> -<li><a href="#org770eaba">Le produit :</a></li> -<li><a href="#org7a41073">Inverse d’une suite :</a></li> -<li><a href="#orgd245f39">Produit d’une suite par un scalaire :</a></li> -</ul> -</li> -<li><a href="#orgd7a311f">Suite bornée :</a></li> -<li><a href="#org2b180d2">Suite majorée :</a></li> -<li><a href="#org7b2e23f">Suite minorée :</a></li> -<li><a href="#orgb167fb6">Suites monotones :</a> -<ul> -<li><a href="#org28ff308">Les suites croissantes :</a></li> -<li><a href="#org89d3d3b">Les suites décroissantes :</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#org65657c4">Série TD N°1 : <i>Oct 6</i></a> -<ul> -<li><a href="#orgac13612">Exo 1 :</a> -<ul> -<li><a href="#orgcb1b828">Ensemble A :</a></li> -<li><a href="#org886db21">Ensemble B :</a></li> -<li><a href="#org8444304">Ensemble C :</a></li> -<li><a href="#org655bbdc">Ensemble D :</a></li> -<li><a href="#orgf122a29">Ensemble E :</a></li> -</ul> -</li> -<li><a href="#org5e26290">Exo 2 :</a> -<ul> -<li><a href="#org62a0c2c">Ensemble A :</a></li> -<li><a href="#orgdde4c67">Ensemble B :</a></li> -<li><a href="#org2abc744">Ensemble C :</a></li> -<li><a href="#orga2cb085">Ensemble D :</a></li> -<li><a href="#orgc6452f9">Ensemble E :</a></li> -</ul> -</li> -<li><a href="#org479db70">Exo 3 :</a> -<ul> -<li><a href="#org9f28f97">Question 1 :</a></li> -<li><a href="#orgb2a312c">Question 2 :</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#orgbd1bb1e">4th cours (Suite) : <i>Oct 10</i></a> -<ul> -<li><a href="#org9b40096">Les suites convergentes</a> -<ul> -<li><a href="#org6a22c62">Remarque :</a></li> -</ul> -</li> -<li><a href="#orga3baa03">Theoreme d’encadrement</a></li> -<li><a href="#orgbbda563">Suites arithmetiques</a> -<ul> -<li><a href="#orgb4756c6">Forme general</a></li> -<li><a href="#orga6494e4">Somme des n premiers termes</a></li> -</ul> -</li> -<li><a href="#org10d88d9">Suites géométriques</a> -<ul> -<li><a href="#orgfe286ce">Forme general</a></li> -<li><a href="#orgaa6b262">Somme des n premiers termes</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#orgeeb4832">5th cours (suite) : <i>Oct 12</i></a> -<ul> -<li><a href="#orge9160fd">Suites adjacentes:</a></li> -<li><a href="#orgaedf3ea">Suites extraites (sous-suites):</a> -<ul> -<li><a href="#org586e8c4">Remarques:</a></li> -</ul> -</li> -<li><a href="#org1ce447c">Suites de Cauchy:</a> -<ul> -<li><a href="#orgd06f7ae">Remarque :</a></li> -</ul> -</li> -<li><a href="#org392a346">Théorème de Bolzano Weirstrass:</a></li> -</ul> -</li> -<li><a href="#org91a748f">Chapitre 3 : Les limites et la continuité <i>Nov 14</i></a> -<ul> -<li><a href="#orgde4196b">Fonction réelle à variable réelle :</a> -<ul> -<li><a href="#orgd68331d">L’ensemble de départ :</a></li> -<li><a href="#org3151412">Les Limites :</a></li> -<li><a href="#org287d826">La continuité :</a></li> -<li><a href="#orgc77ab14">Prolongement par continuité :</a></li> -<li><a href="#org8edfe47">Théorème des valeurs intermédiaires :</a></li> -<li><a href="#orgea41b1c">Fonction croissante :</a></li> -<li><a href="#orgd45a9b4">Injection = Strictement monotonne :</a></li> -<li><a href="#org189c903">Surjection = Continuité :</a></li> -<li><a href="#org07713a2">Bijection :</a></li> -<li><a href="#org7512d26">Théorème de bijection :</a></li> -</ul> -</li> -</ul> -</li> -</ul> -</div> -</div> -<div id="outline-container-org51375f0" class="outline-2"> -<h2 id="org51375f0">Contenu de la Matiére</h2> -<div class="outline-text-2" id="text-org51375f0"> -</div> -<div id="outline-container-orgd074219" class="outline-3"> -<h3 id="orgd074219">Chapitre 1 : Quelque propriétés de ℝ</h3> -<div class="outline-text-3" id="text-orgd074219"> -<ul class="org-ul"> -<li>Structure algébrique de ℝ<br /></li> -<li>L’ordre dans ℝ<br /></li> -<li>Majorant, minorant, borne superieure, borne inférieure<br /></li> -</ul> -</div> -</div> -<div id="outline-container-orgb5220df" class="outline-3"> -<h3 id="orgb5220df">Chapitre 2 : Les suites numériques réelles</h3> -<div class="outline-text-3" id="text-orgb5220df"> -<ul class="org-ul"> -<li>Définition : convergence, opérations sur les suites convergentes<br /></li> -<li>Theoréme de convergence, Theoréme de <span class="underline">_</span> suites, sans suites, extension au limites infinies<br /></li> -<li>Suites de cauchy, suites adjacentes et suites récurentes<br /></li> -</ul> -</div> -</div> -<div id="outline-container-orge7b80f9" class="outline-3"> -<h3 id="orge7b80f9">Chapitre 3 : Limites et continuité des fonctions réelles d’une variable réelle</h3> -<div class="outline-text-3" id="text-orge7b80f9"> -<ul class="org-ul"> -<li>Les limites : définition, opérations sur les limites, les formes inditerminées<br /></li> -<li>La continuité : définition, Theorémes fondamentaux<br /></li> -<li>La continuité informe les fonctions Lepchitziennes<br /></li> -</ul> -</div> -</div> -<div id="outline-container-orgcc6964b" class="outline-3"> -<h3 id="orgcc6964b">Chapitre 4 : La dérivabilité et son interprétation géometrique</h3> -<div class="outline-text-3" id="text-orgcc6964b"> -<ul class="org-ul"> -<li>Opérations sur les fonctions dérivales, Theoréme de Rolle, Theoréme des accroissements finis, régle de L’Hopital et formule de Taylor<br /></li> -</ul> -</div> -</div> -<div id="outline-container-orgea870f0" class="outline-3"> -<h3 id="orgea870f0">Chapitre 5 : Les fonctions trigonométriques réciproques, fonctions hypérboliques réciproques</h3> -<div class="outline-text-3" id="text-orgea870f0"> -<ul class="org-ul"> -<li>Comparaison asymptotique<br /></li> -<li>Symbole de lamdau (lambda ?), et notions des fonctions équivalentes<br /></li> -<li>Développements limites polynominaux (D.L) et opérations sur les D.L<br /></li> -<li>Généralisations des D.L<br /></li> -<li>Application au calcul de limite et l’étude des branches infinies<br /></li> -</ul> -</div> -</div> -</div> -<div id="outline-container-org7dbe2a4" class="outline-2"> -<h2 id="org7dbe2a4">Premier cours : Quelque propriétés de ℝ <i>Sep 26</i> :</h2> -<div class="outline-text-2" id="text-org7dbe2a4"> -</div> -<div id="outline-container-org4b25f0c" class="outline-3"> -<h3 id="org4b25f0c">La loi de composition interne dans E :</h3> -<div class="outline-text-3" id="text-org4b25f0c"> -<p> -@ : E x E —> E<br /> - (x,y) —> x @ y<br /> -</p> - -<p> -@ est une lois de composition interne seulement si :<br /> -</p> - -<p> -<b>∀ x,y ε E</b><br /> -</p> -</div> -<div id="outline-container-orgc048164" class="outline-4"> -<h4 id="orgc048164"><b>Example : Addition</b></h4> -<div class="outline-text-4" id="text-orgc048164"> -<p> -Est ce que l’addition (+) est L.C.I dans ℕ ?<br /> -</p> - -<p> -ℕ x ℕ —> ℕ<br /> -</p> - -<p> -(x,y) —> x + y ? <i>En gros : Pour que l’addition soit une L.C.I dans ℕ, il faut que: quand on additionne <b>n’importe quel</b> chiffre x et y de N, il faut que le résultat appertiens aussi a ℕ</i><br /> -</p> - -<p> -∀ x,y ∈ ℕ , x + y ∈ ℕ <i>En gros: Pour TOUTE valeur de x et y appartenant a ℕ, leur somme est toujours dans ℕ</i><br /> -</p> - -<p> -Donc : + est L.C.I dans ℕ<br /> -</p> -</div> -</div> -<div id="outline-container-orgadeeaa1" class="outline-4"> -<h4 id="orgadeeaa1"><b>Example : soustraction</b></h4> -<div class="outline-text-4" id="text-orgadeeaa1"> -<p> -Est ce que la soustraction (-) est L.C.I dans ℕ?<br /> -</p> - -<p> -ℕ x ℕ —> ℕ<br /> -</p> - -<p> -(x,y) —> x - y ?<br /> -</p> - - -<p> -∃ x , y ∈ ℕ , x - y ∉ ℕ <i>En gros: il existe au moins une valeur de x et y dans ℕ tel que leur différence n’est <b>PAS</b> dans ℕ . tel que : si x est 5, et y c’est 9. Leur différence est -4, qui appartiens pas a ℕ</i><br /> -</p> -</div> -</div> -</div> -<div id="outline-container-orge686f2a" class="outline-3"> -<h3 id="orge686f2a">La loi de composition externe dans E :</h3> -<div class="outline-text-3" id="text-orge686f2a"> -<p> -@ est L.C.E dans E, K est un corps<br /> -</p> - -<p> -K x E —> E<br /> -</p> - -<p> -(a,x) —> a @ x<br /> -</p> - -<p> -∀ (a , x) ∈ K x E , a @ x ∈ E<br /> -</p> -</div> -</div> -<div id="outline-container-org96fc192" class="outline-3"> -<h3 id="org96fc192">Groupes :</h3> -<div class="outline-text-3" id="text-org96fc192"> -<p> -<i>Soit E un ensemble, soit @ une L.C.I dans E</i><br /> -</p> - -<p> -(E, @) est un groupe Si :<br /> -</p> -</div> -<div id="outline-container-org9cae959" class="outline-4"> -<h4 id="org9cae959">Il contiens un élement neutre</h4> -<div class="outline-text-4" id="text-org9cae959"> -<p> -∀ x ∈ E ; ∃ e ∈ E<br /> -</p> - -<p> -x @ e = e @ x = x<br /> -</p> - -<p> -On appelle <b>e</b> élement neutre<br /> -</p> - -<p> -<i>Ex: (ℕ,+) accepte un élement neutre, qui est 0, parceque x + 0 = 0 + x = x….cependent (ℕ,+) n’est pas un groupe. La raison est dans la prochaine condition</i><br /> -</p> -</div> -</div> -<div id="outline-container-orgfc1fc7b" class="outline-4"> -<h4 id="orgfc1fc7b">Il contiens un élément symétrique</h4> -<div class="outline-text-4" id="text-orgfc1fc7b"> -<p> -∀ x ∈ E ; ∃ x’ ∈ E ; x @ x’ = x’ @ x = e<br /> -</p> - -<p> -On appelle <b>x’</b> élèment symétrique<br /> -</p> - -<p> -<i>Dans l’example en haut, on remarque qu’il n’y ya pas de chiffre x’ pour chaque chiffre x, qui est, l’hors de leur addition est egal a e (0), tout simplement car:</i><br /> -</p> - -<p> -<i>x + x’ = e ; x + x’ = 0 ; x = -x’</i><br /> -</p> - -<p> -<b>Or, Dans ℕ, on a pas de nombres négatifs</b><br /> -</p> -</div> -</div> -<div id="outline-container-orge76674f" class="outline-4"> -<h4 id="orge76674f">@ est cummutative :</h4> -<div class="outline-text-4" id="text-orge76674f"> -<p> -∀ (x , x’) ∈ E x E ; x @ x’ = x’ @ x<br /> -</p> - -<p> -<i>L’addition est cummutative, la soustraction ne l’es pas. 5 + 3 ou 3 + 5 est pareil, mais 5 - 3 et 3 - 5 sont différents</i><br /> -</p> -</div> -</div> -</div> -<div id="outline-container-orgde40808" class="outline-3"> -<h3 id="orgde40808">Anneaux :</h3> -<div class="outline-text-3" id="text-orgde40808"> -<p> -Soit E un ensemble, (E , @ , !) est un anneau si :<br /> -</p> -</div> -<div id="outline-container-org6960733" class="outline-4"> -<h4 id="org6960733">(E ; @) est un groupe cummutatif</h4> -</div> -<div id="outline-container-org3dd13c2" class="outline-4"> -<h4 id="org3dd13c2">! est une loi associative :</h4> -<div class="outline-text-4" id="text-org3dd13c2"> -<p> -∀ x , y , z ∈ E<br /> -</p> - -<p> -(x ! y) ! z = x ! (y ! z)<br /> -</p> -</div> -</div> -<div id="outline-container-org96e7790" class="outline-4"> -<h4 id="org96e7790">Distribution de ! par rapport à @ :</h4> -<div class="outline-text-4" id="text-org96e7790"> -<p> -∀ x , y , z ∈ E<br /> -</p> - -<p> -(x @ y) ! z = ( x ! z ) @ ( y ! z )<br /> -</p> -</div> -</div> -<div id="outline-container-orgaaceb67" class="outline-4"> -<h4 id="orgaaceb67">L’existance d’un élèment neutre de ! :</h4> -<div class="outline-text-4" id="text-orgaaceb67"> -<p> -∀ x ∈ E , ∃ e ∈ E , x ! e = e ! x = x<br /> -</p> -</div> -</div> -<div id="outline-container-org07575e5" class="outline-4"> -<h4 id="org07575e5">! est cummutative :</h4> -<div class="outline-text-4" id="text-org07575e5"> -<p> -∀ x , y ∈ E , x ! y = y ! x<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org4dde6a2" class="outline-3"> -<h3 id="org4dde6a2">Corps :</h3> -<div class="outline-text-3" id="text-org4dde6a2"> -<p> -(E , @ , !) est un corps si les 5 conditions en haut sont vérifiées + cette condition :<br /> -</p> -</div> -<div id="outline-container-orga3ea966" class="outline-4"> -<h4 id="orga3ea966">La symétrie :</h4> -<div class="outline-text-4" id="text-orga3ea966"> -<p> -∀ x ∈ E ; ∃ x’ ∈ E , x ! x’ = x’ ! x = e<br /> -</p> - -<p> -x’ est l’élément symétrique de x par rapport à !<br /> -(sauf élément neutre première lois )<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org316172f" class="outline-3"> -<h3 id="org316172f">Exercice : (ℝ, +, x) corps ou pas ?</h3> -<div class="outline-text-3" id="text-org316172f"> -</div> -<div id="outline-container-org4ed9aef" class="outline-4"> -<h4 id="org4ed9aef">Est-ce un Anneau ?</h4> -<div class="outline-text-4" id="text-org4ed9aef"> -<ul class="org-ul"> -<li>(ℝ, +) est un groupe commutatif<br /></li> -<li>x est une loi associative : (a x b) x c = a x (b x c)<br /></li> -<li>On peut distribuer x par rapport a + : (a + b) x c = (a x c) + (b x c)<br /></li> -<li>Il existe un élément neutre de x which is 1 : a x 1 = 1 x a = a<br /></li> -<li>La multiplication est commutative : a x b = b x a<br /></li> -</ul> - -<p> -Oui c’est un anneau<br /> -</p> -</div> -</div> -<div id="outline-container-org248a5ea" class="outline-4"> -<h4 id="org248a5ea">Est-ce un corps ?</h4> -<div class="outline-text-4" id="text-org248a5ea"> -<ul class="org-ul"> -<li>Oui : ∀ x ∈ ℝ\{e} ; x * x’ = 1<br /></li> -</ul> -</div> -</div> -</div> -</div> -<div id="outline-container-org0b3fce2" class="outline-2"> -<h2 id="org0b3fce2">2nd cours :L’ordre dans ℝ, Majorant, minorant, borne superieure, borne inférieure <i>Oct 3</i> :</h2> -<div class="outline-text-2" id="text-org0b3fce2"> -</div> -<div id="outline-container-orga3c4b3c" class="outline-3"> -<h3 id="orga3c4b3c">L’ordre dans ℝ</h3> -<div class="outline-text-3" id="text-orga3c4b3c"> -<p> -(ℝ, +, x) est un corps, Soit R une relation d’ordre dans ℝ si :<br /> -</p> - -<ol class="org-ol"> -<li><p> -R est antisymétrique :<br /> -</p> - -<p> -∀ x, y ℝ ; (x R y et y R x) ⇒ (x = y)<br /> -</p></li> - -<li><p> -R est reflexive :<br /> -</p> - -<p> -∀ x ∈ ℝ ; x R x<br /> -</p></li> - -<li>R est transitive :<br /> -∀ x, y, z ∈ ℝ , (x R y and y R z) ⇒ x R z<br /></li> -</ol> -</div> -<div id="outline-container-org9b04907" class="outline-4"> -<h4 id="org9b04907">Exemples :</h4> -<div class="outline-text-4" id="text-org9b04907"> -</div> -<ul class="org-ul"> -<li><a id="org10940af"></a>Exemple numéro 1:<br /> -<div class="outline-text-5" id="text-org10940af"> -<p> -(ℝ , +, x) est un corps. Est ce la relation < est une relation d’ordre dans ℝ ?<br /> -</p> - - -<p> -Non, pourquoi ? parce que elle est pas réflexive : ∀ x ∈ ℝ, x < x <b><b>is obviously false</b></b><br /> -</p> -</div> -</li> -<li><a id="org47b3e4d"></a>Exemple numéro 2:<br /> -<div class="outline-text-5" id="text-org47b3e4d"> -<p> -(ℝ , +, x) est un corps. Est ce la relation ≥ est une relation d’ordre dans ℝ ?<br /> -</p> - -<ol class="org-ol"> -<li>(Antisymétrique) ∀ x, y ℝ ; (x ≥ y AND y ≥ x) ⇒ x = y is true<br /></li> -<li>(Réflexive) ∀ x, y ℝ ; x ≥ x is true<br /></li> -<li>(Transitive) ∀ x, y, z ℝ ; (x ≥ y AND y ≥ z) ⇒ x ≥ z is also true<br /></li> -</ol> -</div> -</li> -</ul> -</div> -</div> -<div id="outline-container-org824efff" class="outline-3"> -<h3 id="org824efff">Majorant, minorant, borne supérieure, borne inférieure</h3> -<div class="outline-text-3" id="text-org824efff"> -</div> -<div id="outline-container-org34c228b" class="outline-4"> -<h4 id="org34c228b">Majorant:</h4> -<div class="outline-text-4" id="text-org34c228b"> -<p> -Soit E un sous-ensemble de ℝ (E ⊆ ℝ)<br /> -</p> - - -<p> -Soit a ∈ ℝ, a est un majorant de E Si :∀ x ∈ E , x ≤ a<br /> -</p> -</div> -</div> -<div id="outline-container-orgc832fb0" class="outline-4"> -<h4 id="orgc832fb0">Minorant:</h4> -<div class="outline-text-4" id="text-orgc832fb0"> -<p> -Soit E un sous-ensemble de ℝ (E ⊆ ℝ)<br /> -</p> - - -<p> -Soit b ∈ ℝ, b est un minorant de E Si :∀ x ∈ E , x ≥ b<br /> -</p> -</div> -</div> -<div id="outline-container-org3cb02e2" class="outline-4"> -<h4 id="org3cb02e2">Borne supérieure:</h4> -<div class="outline-text-4" id="text-org3cb02e2"> -<p> -La borne supérieure est le plus petit des majorants <i>Sup(E) = Borne supérieure</i><br /> -</p> -</div> -</div> -<div id="outline-container-orgef4458e" class="outline-4"> -<h4 id="orgef4458e">Borne inférieure:</h4> -<div class="outline-text-4" id="text-orgef4458e"> -<p> -La borne inférieure est le plus grand des minorant <i>Inf (E) = Borne inférieure</i><br /> -</p> -</div> -</div> -<div id="outline-container-org2b2908f" class="outline-4"> -<h4 id="org2b2908f">Maximum :</h4> -<div class="outline-text-4" id="text-org2b2908f"> -<p> -E ⊆ ℝ, a est un maximum de E (Max(E)) Si : a ∈ E ; ∀x ∈ E, x ≤ a.<br /> -</p> -</div> -</div> -<div id="outline-container-org1410a06" class="outline-4"> -<h4 id="org1410a06">Minimum :</h4> -<div class="outline-text-4" id="text-org1410a06"> -<p> -E ⊆ ℝ, b est un minimum de E (Min(E)) Si : b ∈ E ; ∀x ∈ E, x ≥ b.<br /> -</p> -</div> -</div> -<div id="outline-container-orgd1fcd4e" class="outline-4"> -<h4 id="orgd1fcd4e">Remarques :</h4> -<div class="outline-text-4" id="text-orgd1fcd4e"> -<p> -A et B deux ensembles bornés (Minoré et Majoré) :<br /> -</p> -<ol class="org-ol"> -<li>A ∪ B est borné<br /></li> -<li>A ∩ B est borné<br /></li> -<li>Sup(A ∪ B)= Max(sup A, sup B)<br /></li> -<li>Inf (A ∩ B)= Min(inf A, inf B)<br /></li> -<li>Sup(A ∩ B)= Min(sup A, sup B) <i>Le plus petit des Supérieur de A et B</i><br /></li> -<li>Inf (A ∩ B)= Max(inf A, inf B) <i>Le plus grand des inférieur de A et B</i><br /></li> -</ol> -</div> -</div> -</div> -</div> -<div id="outline-container-orgc939931" class="outline-2"> -<h2 id="orgc939931">3rd cours :Les suites numériques <i>Oct 5</i> :</h2> -<div class="outline-text-2" id="text-orgc939931"> -</div> -<div id="outline-container-org8607984" class="outline-4"> -<h4 id="org8607984">Définition :</h4> -<div class="outline-text-4" id="text-org8607984"> -<p> -Soit (Un)n ∈ ℕ une suite numérique , (Un)n est une application de ℕ dans ℝ:<br /> -</p> - - -<p> -ℕ -—> ℝ<br /> -</p> - - -<p> -n -—> U(n) = Un<br /> -</p> - -<ol class="org-ol"> -<li>(Un) ou (Un)n ∈ ℝ : une suite<br /></li> -<li>Un : terme général<br /></li> -</ol> -</div> -<ul class="org-ul"> -<li><a id="org51d3f5d"></a>Exemple :<br /> -<div class="outline-text-6" id="text-org51d3f5d"> -<p> -U : ℕ* -—> ℝ<br /> -</p> - - -<p> -n -—> 1/n<br /> -</p> - - -<p> -(Un) est une suite définit par Un = 1/n<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-orgcc2100f" class="outline-4"> -<h4 id="orgcc2100f">Définition N°2 :</h4> -<div class="outline-text-4" id="text-orgcc2100f"> -<p> -On peut définir une suite â partir d’une relation de récurrence entre deux termes successifs et le premier terme.<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org6b68ae0"></a>Exemple :<br /> -<div class="outline-text-6" id="text-org6b68ae0"> -<p> -U(n+1) = Un /2<br /> -</p> - - -<p> -U(1)= 1<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org69f8c52" class="outline-3"> -<h3 id="org69f8c52">Opérations sur les suites :</h3> -<div class="outline-text-3" id="text-org69f8c52"> -</div> -<div id="outline-container-orgf01d039" class="outline-4"> -<h4 id="orgf01d039">La somme :</h4> -<div class="outline-text-4" id="text-orgf01d039"> -<p> -Soient (Un) et (Vn) deux suites, la somme de (Un) et (Vn) est une suite de terme général Un + Vn<br /> -</p> -</div> -</div> -<div id="outline-container-org770eaba" class="outline-4"> -<h4 id="org770eaba">Le produit :</h4> -<div class="outline-text-4" id="text-org770eaba"> -<p> -Soient (Un)n et (Vn)n deux suites alors (Un) x (Vn) est une autre suite de terme général Un x Vn<br /> -</p> -</div> -</div> -<div id="outline-container-org7a41073" class="outline-4"> -<h4 id="org7a41073">Inverse d’une suite :</h4> -<div class="outline-text-4" id="text-org7a41073"> -<p> -Soit Un une suite de terme général Un alors l’inverse de (Un) est une autre suite (Vn) = 1/(Un) de terme général de Vn = 1/Un<br /> -</p> -</div> -</div> -<div id="outline-container-orgd245f39" class="outline-4"> -<h4 id="orgd245f39">Produit d’une suite par un scalaire :</h4> -<div class="outline-text-4" id="text-orgd245f39"> -<p> -Soit (Un) une suite de T.G Un<br /> -</p> - - -<p> -∀ λ ∈ ℝ , λ(Un) n ∈ ℕ est une suite de T.G Vn= λUn<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-orgd7a311f" class="outline-3"> -<h3 id="orgd7a311f">Suite bornée :</h3> -<div class="outline-text-3" id="text-orgd7a311f"> -<p> -Une suite (Un) est bornée si (Un) majorée et minorée<br /> -</p> -</div> -</div> -<div id="outline-container-org2b180d2" class="outline-3"> -<h3 id="org2b180d2">Suite majorée :</h3> -<div class="outline-text-3" id="text-org2b180d2"> -<p> -Soit (Un) une suite<br /> -</p> - - -<p> -U : (Un) est majorée par M ∈ ℝ ; ∀ n ∈ ℕ ; ∃ M ∈ ℝ , Un ≤ M<br /> -</p> -</div> -</div> -<div id="outline-container-org7b2e23f" class="outline-3"> -<h3 id="org7b2e23f">Suite minorée :</h3> -<div class="outline-text-3" id="text-org7b2e23f"> -<p> -Soit (Un) une suite<br /> -</p> - - -<p> -U : (Un) est minorée par M ∈ ℝ ; ∀ n ∈ ℕ ; ∃ M ∈ ℝ , Un ≥ M<br /> -</p> -</div> -</div> -<div id="outline-container-orgb167fb6" class="outline-3"> -<h3 id="orgb167fb6">Suites monotones :</h3> -<div class="outline-text-3" id="text-orgb167fb6"> -</div> -<div id="outline-container-org28ff308" class="outline-4"> -<h4 id="org28ff308">Les suites croissantes :</h4> -<div class="outline-text-4" id="text-org28ff308"> -<p> -Soit (Un)n est une suite<br /> -</p> - - -<p> -(Un) est croissante si : ∀ n ∈ ℕ ; U(n+1) - Un ≥ 0 ⇔ Un+1 ≥ Un<br /> -</p> -</div> -</div> -<div id="outline-container-org89d3d3b" class="outline-4"> -<h4 id="org89d3d3b">Les suites décroissantes :</h4> -<div class="outline-text-4" id="text-org89d3d3b"> -<p> -Soit (Un)n est une suite<br /> -</p> - - -<p> -(Un) est décroissante si : ∀ n ∈ ℕ ; U(n+1) - Un ≤ 0 ⇔ Un+1 ≤ Un<br /> -</p> -</div> -</div> -</div> -</div> -<div id="outline-container-org65657c4" class="outline-2"> -<h2 id="org65657c4">Série TD N°1 : <i>Oct 6</i></h2> -<div class="outline-text-2" id="text-org65657c4"> -</div> -<div id="outline-container-orgac13612" class="outline-3"> -<h3 id="orgac13612">Exo 1 :</h3> -<div class="outline-text-3" id="text-orgac13612"> -</div> -<div id="outline-container-orgcb1b828" class="outline-4"> -<h4 id="orgcb1b828">Ensemble A :</h4> -<div class="outline-text-4" id="text-orgcb1b828"> -<p> -A = {-1/n , n ∈ ℕ *}<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org47ef9df"></a>Borne inférieure<br /> -<div class="outline-text-5" id="text-org47ef9df"> -<p> -∀ n ∈ ℕ* , -1/n ≥ -1 . -1 est la borne inférieure de l’ensemble A<br /> -</p> -</div> -</li> -<li><a id="orgd07d16e"></a>Minimum :<br /> -<div class="outline-text-5" id="text-orgd07d16e"> -<p> -∀ n ∈ ℕ* , -1/n ≥ -1 . -1 est le Minimum de l’ensemble A<br /> -</p> -</div> -</li> -<li><a id="org04fdb17"></a>Borne supérieure :<br /> -<div class="outline-text-5" id="text-org04fdb17"> -<p> -∀ n ∈ ℕ* , -1/n ≤ 0 . 0 est la borne supérieure de l’ensemble A<br /> -</p> -</div> -</li> -<li><a id="org8029216"></a>Maximum :<br /> -<div class="outline-text-5" id="text-org8029216"> -<p> -L’ensemble A n’as pas de maximum<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org886db21" class="outline-4"> -<h4 id="org886db21">Ensemble B :</h4> -<div class="outline-text-4" id="text-org886db21"> -<p> -B = [-1 , 3[ ∩ ℚ<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orgcde09bc"></a>Borne inférieure :<br /> -<div class="outline-text-5" id="text-orgcde09bc"> -<p> -Inf (B) = Max(inf ([-1 , 3[) , inf (ℚ))<br /> -</p> - - -<p> -Puisse que ℚ n’as pas de Borne inférieure, donc par convention c’est <b>-∞</b>,<br /> -</p> - - -<p> -<b>Inf (B) = -1</b><br /> -</p> -</div> -</li> -<li><a id="orgd0b46a7"></a>Borne supérieure :<br /> -<div class="outline-text-5" id="text-orgd0b46a7"> -<p> -Sup(B) = Min(sup([-1 ,3[) , sup(ℚ))<br /> -</p> - - -<p> -Puisse que ℚ n’as pas de Borne supérieure, donc par convention c’est <b>+∞</b>,<br /> -</p> - - -<p> -<b>Sup(B) = 3</b><br /> -</p> -</div> -</li> -<li><a id="orgdd05682"></a>Minimum :<br /> -<div class="outline-text-5" id="text-orgdd05682"> -<p> -<b>Min(B) = -1</b><br /> -</p> -</div> -</li> -<li><a id="org2f56d5c"></a>Maximum :<br /> -<div class="outline-text-5" id="text-org2f56d5c"> -<p> -L’ensemble B n’as pas de Maximum<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org8444304" class="outline-4"> -<h4 id="org8444304">Ensemble C :</h4> -<div class="outline-text-4" id="text-org8444304"> -<p> -C = {3n ,n ∈ ℕ}<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org71172ed"></a>Borne inférieure :<br /> -<div class="outline-text-5" id="text-org71172ed"> -<p> -Inf (C) = 0<br /> -</p> -</div> -</li> -<li><a id="orgd7dc786"></a>Borne supérieure :<br /> -<div class="outline-text-5" id="text-orgd7dc786"> -<p> -Sup(C) = +∞<br /> -</p> -</div> -</li> -<li><a id="org48d58aa"></a>Minimum :<br /> -<div class="outline-text-5" id="text-org48d58aa"> -<p> -Min(C) = 0<br /> -</p> -</div> -</li> -<li><a id="org2f05d94"></a>Maximum :<br /> -<div class="outline-text-5" id="text-org2f05d94"> -<p> -L’ensemble C n’as pas de Maximum<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org655bbdc" class="outline-4"> -<h4 id="org655bbdc">Ensemble D :</h4> -<div class="outline-text-4" id="text-org655bbdc"> -<p> -D = {1 - 1/n , n ∈ ℕ*}<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orgcb1e6fa"></a>Borne inférieure :<br /> -<div class="outline-text-5" id="text-orgcb1e6fa"> -<p> -Inf (D)= 0<br /> -</p> -</div> -</li> -<li><a id="org865b9b0"></a>Borne supérieure :<br /> -<div class="outline-text-5" id="text-org865b9b0"> -<p> -Sup(D)= 1<br /> -</p> -</div> -</li> -<li><a id="org9a1de73"></a>Minimum :<br /> -<div class="outline-text-5" id="text-org9a1de73"> -<p> -Min(D)= 0<br /> -</p> -</div> -</li> -<li><a id="org1987362"></a>Maximum :<br /> -<div class="outline-text-5" id="text-org1987362"> -<p> -L’ensemble D n’as pas de Maximum<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-orgf122a29" class="outline-4"> -<h4 id="orgf122a29">Ensemble E :</h4> -<div class="outline-text-4" id="text-orgf122a29"> -<p> -E = { [2n + (-1)^n]/ n + 1 , n ∈ ℕ }<br /> -</p> - - -<p> -<b>Les valeurs que E peut prendre sont : “(2n + 1)/(n+1)” Si n est pair, et “(2n - 1)/(n+1)” si n est impair</b><br /> -</p> - - -<p> -<b>On définit un ensemble F et G : F = { (2n + 1)/ (n+1) , n ∈ 2k}, G = { (2n - 1)/(n+1), n ∈ 2k+1}</b><br /> -</p> - - -<p> -<b>Donc E = F ∪ G</b><br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org45d0ef4"></a>Borne inférieure :<br /> -<div class="outline-text-5" id="text-org45d0ef4"> -<p> -Inf (E) = Min(inf (F), inf (G))<br /> -</p> - - -<p> -Inf (F) = 1 ; Inf (G) = -1<br /> -</p> - - -<p> -<b>Inf (E)= -1</b><br /> -</p> -</div> -</li> -<li><a id="org5ef627a"></a>Borne supérieure :<br /> -<div class="outline-text-5" id="text-org5ef627a"> -<p> -Sup(E) = Max(sup(F), sup(G))<br /> -</p> - - -<p> -sup(F) = +∞ ; sup(G) = +∞<br /> -</p> - - -<p> -<b>Sup(E)= +∞</b><br /> -</p> -</div> -</li> -<li><a id="orgef4c9c4"></a>Minimum :<br /> -<div class="outline-text-5" id="text-orgef4c9c4"> -<p> -Min(E)= -1<br /> -</p> -</div> -</li> -<li><a id="org49b27f7"></a>Maximum :<br /> -<div class="outline-text-5" id="text-org49b27f7"> -<p> -E n’as pas de maximum<br /> -</p> -</div> -</li> -</ul> -</div> -</div> -<div id="outline-container-org5e26290" class="outline-3"> -<h3 id="org5e26290">Exo 2 :</h3> -<div class="outline-text-3" id="text-org5e26290"> -</div> -<div id="outline-container-org62a0c2c" class="outline-4"> -<h4 id="org62a0c2c">Ensemble A :</h4> -<div class="outline-text-4" id="text-org62a0c2c"> -<p> -A = {x ∈ ℝ , 0 < x <√3}<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org89ac7fa"></a>Borné<br /> -<div class="outline-text-5" id="text-org89ac7fa"> -<p> -<b>Oui</b>, Inf (A)= 0 ; Sup(A)=√3<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-orgdde4c67" class="outline-4"> -<h4 id="orgdde4c67">Ensemble B :</h4> -<div class="outline-text-4" id="text-orgdde4c67"> -<p> -B = { x ∈ ℝ , 1/2 < sin x <√3/2} ;<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org2a13712"></a>Borné<br /> -<div class="outline-text-5" id="text-org2a13712"> -<p> -<b>∀ x ∈ B, sin x > 1/2 ∴ Inf (B)= 1/2</b><br /> -</p> - - -<p> -<b>∀ x ∈ B, sin x < √3/2 ∴ Sup(B)= √3/2</b><br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org2abc744" class="outline-4"> -<h4 id="org2abc744">Ensemble C :</h4> -<div class="outline-text-4" id="text-org2abc744"> -<p> -C = {x ∈ ℝ , x³ > 3}<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org6a12e74"></a>Minoré<br /> -<div class="outline-text-5" id="text-org6a12e74"> -<p> -<b>∀ x ∈ C, x³ > 3 ∴ Inf (C)= 3</b><br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-orga2cb085" class="outline-4"> -<h4 id="orga2cb085">Ensemble D :</h4> -<div class="outline-text-4" id="text-orga2cb085"> -<p> -D = {x ∈ ℝ , e^x < 1/2}<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org42d90c1"></a>Borné<br /> -<div class="outline-text-5" id="text-org42d90c1"> -<p> -<b>∀ x ∈ C, e^x > 0 ∴ Inf (C)= 0</b><br /> -</p> - - -<p> -<b>∀ x ∈ C, e^x < 1/2 ∴ Sup(C)= 1/2</b><br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-orgc6452f9" class="outline-4"> -<h4 id="orgc6452f9">Ensemble E :</h4> -<div class="outline-text-4" id="text-orgc6452f9"> -<p> -E = {x ∈ ℝ , ∃ p ∈ ℕ* : x = √2/p}<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org8696739"></a>Majoré<br /> -<div class="outline-text-5" id="text-org8696739"> -<p> -p = √2/x . Donc : <b>Sup(E)=1</b><br /> -</p> -</div> -</li> -</ul> -</div> -</div> -<div id="outline-container-org479db70" class="outline-3"> -<h3 id="org479db70">Exo 3 :</h3> -<div class="outline-text-3" id="text-org479db70"> -<p> -U0 = 3/2 ; U(n+1) = (Un - 1)² + 1<br /> -</p> -</div> -<div id="outline-container-org9f28f97" class="outline-4"> -<h4 id="org9f28f97">Question 1 :</h4> -<div class="outline-text-4" id="text-org9f28f97"> -<p> -Montrer que : ∀ n ∈ ℕ , 1 < Un < 2 .<br /> -</p> - - -<p> -<b>(Un - 1)² ≥ 0 <i>Parce que c’est un carré</i></b><br /> -</p> - - -<p> -<b>(Un - 1)² + 1 > 1</b> ; <b>U(n+1) ≥ 1</b><br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orgf620b41"></a>Raisonnement par récurrence :<br /> -<div class="outline-text-5" id="text-orgf620b41"> -<p> -P(n) : ∀ n ∈ ℕ ; 1 < Un < 2<br /> -</p> - - -<p> -P(0) est vraie : 1 < 3/2 < 2<br /> -</p> - - -<p> -On suppose que P(n) est vraie et on vérifie P(n+1) pour une contradiction<br /> -</p> - - -<p> -1< Un < 2 ; 0 < Un - 1 < 1 ; 0 < (Un - 1)² < 1 ; 1 < (Un - 1)² + 1< 2 ; <b>1 < U(n+1) < 2</b> Donc elle est correcte<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-orgb2a312c" class="outline-4"> -<h4 id="orgb2a312c">Question 2 :</h4> -<div class="outline-text-4" id="text-orgb2a312c"> -<p> -Montrer que (Un)n est strictement monotone :<br /> -</p> - - -<p> -<b>U(n+1) - Un = (Un - 1)² + 1 - Un</b> ; <b>U(n+1) - Un = Un² + 1 - 2Un + 1 - Un</b> ; <b>U(n+1) - Un = Un² - 3Un + 2</b><br /> -</p> - - -<p> -On étudie <b>Un² - 3Un + 2</b> sur l’intervalle ]1, 2[ : Un² - 3Un + 2 = 0 est une équation du 2nd ordre, <b>Δ = 1</b> , elle accepte deux solutions : Un = 1 et Un = 2<br /> -</p> - - -<p> -On déduit que <b>Un² - 3Un + 2</b> est négatif sur [1 , 2] et positif en dehors, donc <b>∀ 1 < Un < 2 , Un² - 3Un + 2 < 0</b> ; <b>∀ 1 < Un < 2 , U(n+1) - Un < 0</b> ; <b>∀ 1 < Un < 2 , U(n+1) < Un</b> Donc (Un)n est une suite strictement monotonne décroissante<br /> -</p> -</div> -</div> -</div> -</div> -<div id="outline-container-orgbd1bb1e" class="outline-2"> -<h2 id="orgbd1bb1e">4th cours (Suite) : <i>Oct 10</i></h2> -<div class="outline-text-2" id="text-orgbd1bb1e"> -</div> -<div id="outline-container-org9b40096" class="outline-3"> -<h3 id="org9b40096">Les suites convergentes</h3> -<div class="outline-text-3" id="text-org9b40096"> -<p> -Soit (Un)n est une suite convergente si lim Un n–> +∞ = l<br /> -</p> -</div> -<div id="outline-container-org6a22c62" class="outline-4"> -<h4 id="org6a22c62">Remarque :</h4> -<div class="outline-text-4" id="text-org6a22c62"> -<ol class="org-ol"> -<li>Un est une suite convergente alors Un est bornee<br /></li> -<li>Un est une suite convergente lim Un n—> +∞ = l ⇔ lim |Un| n—> +∞ = |l|<br /></li> -<li>Un est une suite majoree et croissante ⇒ Un converge<br /></li> -<li>Un est une suite minoree et decroissante ⇒ Un converge<br /></li> -<li>Soient (Un) et (Vn) deux suites convergentes, alors<br /> -<ol class="org-ol"> -<li>Un + Vn est convergente<br /></li> -<li>Un * Vn est convergente<br /></li> -<li>∀λ ∈ ℝ , (λUn) converge<br /></li> -</ol></li> -<li>Soit Un est une suite bornee et soit Vn une suite. lim Vn n->+∞ = 0 Alors lim Vn * Un n-> +∞ = 0<br /></li> -</ol> -</div> -</div> -</div> -<div id="outline-container-orga3baa03" class="outline-3"> -<h3 id="orga3baa03">Theoreme d’encadrement</h3> -<div class="outline-text-3" id="text-orga3baa03"> -<p> -Soient Un Vn et Wn trois suites ∀n ∈ ℕ, Un ≤ Vn ≤ Wn . et lim Un n->∞ = lim Wn n-> +∞ = l ⇒ lim Vn n-> +∞ = l<br /> -</p> -</div> -</div> -<div id="outline-container-orgbbda563" class="outline-3"> -<h3 id="orgbbda563">Suites arithmetiques</h3> -<div class="outline-text-3" id="text-orgbbda563"> -<p> -Un est une suite arithmetique si : U(n+1) = Un + r ; r etant la raison de la suite<br /> -</p> -</div> -<div id="outline-container-orgb4756c6" class="outline-4"> -<h4 id="orgb4756c6">Forme general</h4> -<div class="outline-text-4" id="text-orgb4756c6"> -<p> -<b>Un = U0 + nr</b> ; <b>Un = Up + (n - p)r</b><br /> -</p> -</div> -</div> -<div id="outline-container-orga6494e4" class="outline-4"> -<h4 id="orga6494e4">Somme des n premiers termes</h4> -<div class="outline-text-4" id="text-orga6494e4"> -<p> -Un est une suite arithmetique, Sn = [(U0 + Un)(n + 1)]/2<br /> -</p> - - -<p> -Sn = (n, k = 0)ΣUk est une somme partielle et lim Sn n->+∞ = k≥0ΣUk est une serie<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org10d88d9" class="outline-3"> -<h3 id="org10d88d9">Suites géométriques</h3> -<div class="outline-text-3" id="text-org10d88d9"> -</div> -<div id="outline-container-orgfe286ce" class="outline-4"> -<h4 id="orgfe286ce">Forme general</h4> -<div class="outline-text-4" id="text-orgfe286ce"> -<p> -<b>Un = U0 x r^n</b><br /> -</p> -</div> -</div> -<div id="outline-container-orgaa6b262" class="outline-4"> -<h4 id="orgaa6b262">Somme des n premiers termes</h4> -<div class="outline-text-4" id="text-orgaa6b262"> -<p> -n ∈ ℕ\{1} Sn = U0 (1 - r^(n+1))/1-r<br /> -</p> -</div> -</div> -</div> -</div> -<div id="outline-container-orgeeb4832" class="outline-2"> -<h2 id="orgeeb4832">5th cours (suite) : <i>Oct 12</i></h2> -<div class="outline-text-2" id="text-orgeeb4832"> -</div> -<div id="outline-container-orge9160fd" class="outline-3"> -<h3 id="orge9160fd">Suites adjacentes:</h3> -<div class="outline-text-3" id="text-orge9160fd"> -<p> -Soient (Un) et (Vn) deux suites, elles sont adjacentes si:<br /> -</p> -<ol class="org-ol"> -<li>(Un) est croissante et (Vn) est décroissante<br /></li> -<li>Un ≤ Vn<br /></li> -<li>lim (Un - Vn) n->+∞ = 0<br /></li> -</ol> -</div> -</div> -<div id="outline-container-orgaedf3ea" class="outline-3"> -<h3 id="orgaedf3ea">Suites extraites (sous-suites):</h3> -<div class="outline-text-3" id="text-orgaedf3ea"> -<p> -Soit (Un) une suite: ;U: ℕ -—> ℝ ; n -—> Un ;ϕ: ℕ -—> ℕ ; n -—> ϕn ;(U(ϕ(n))) est appelée une sous suite de (Un) ou bien une suite extraite.<br /> -</p> -</div> -<div id="outline-container-org586e8c4" class="outline-4"> -<h4 id="org586e8c4">Remarques:</h4> -<div class="outline-text-4" id="text-org586e8c4"> -<ol class="org-ol"> -<li>Si (Un) converge ⇒ ∀ n ∈ ℕ , U(ϕ(n)) converge aussi.<br /></li> -<li>Mais le contraire n’es pas toujours vrais.<br /></li> -<li>U(2n) et U(2n+1) convergent vers la même limite (l), alors Un aussi converge vers l<br /></li> -</ol> -</div> -</div> -</div> -<div id="outline-container-org1ce447c" class="outline-3"> -<h3 id="org1ce447c">Suites de Cauchy:</h3> -<div class="outline-text-3" id="text-org1ce447c"> -<p> -(Un) n ∈ ℕ est une suite de Cauchy Si ; ;∀ ε > 0 , ∃ N ∈ ℕ ; ∀ n > m > N ; |Un - Um| < ε<br /> -</p> -</div> -<div id="outline-container-orgd06f7ae" class="outline-4"> -<h4 id="orgd06f7ae">Remarque :</h4> -<div class="outline-text-4" id="text-orgd06f7ae"> -<ol class="org-ol"> -<li>Toute suite convergente est une suite de Cauchy et toute suite Cauchy est une suite convergente<br /></li> -</ol> -</div> -</div> -</div> -<div id="outline-container-org392a346" class="outline-3"> -<h3 id="org392a346">Théorème de Bolzano Weirstrass:</h3> -<div class="outline-text-3" id="text-org392a346"> -<p> -On peut extraire une sous suite convergente de toute suite bornée<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org91a748f" class="outline-2"> -<h2 id="org91a748f">Chapitre 3 : Les limites et la continuité <i>Nov 14</i></h2> -<div class="outline-text-2" id="text-org91a748f"> -</div> -<div id="outline-container-orgde4196b" class="outline-3"> -<h3 id="orgde4196b">Fonction réelle à variable réelle :</h3> -<div class="outline-text-3" id="text-orgde4196b"> -<p> -Soit f : I –> ℝ , I ⊂= ℝ<br /> - x –> f (x)<br /> -</p> -</div> -<div id="outline-container-orgd68331d" class="outline-4"> -<h4 id="orgd68331d">L’ensemble de départ :</h4> -<div class="outline-text-4" id="text-orgd68331d"> -<p> -L’ensemble de définition (Df)<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org5899912"></a>Propriétés:<br /> -<div class="outline-text-5" id="text-org5899912"> -<p> -Soit f et g deux fonctions :<br /> -f : I –> ℝ<br /> - x –> f (x)<br /> -</p> - -<p> -g : I –> ℝ<br /> - x –> g(x)<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orge1e9b5a"></a>1) f+g<br /> -<div class="outline-text-6" id="text-orge1e9b5a"> -<p> -(g+f): I –> ℝ<br /> - x –> (f+g)(x) = f (x) + g(x)<br /> -</p> -</div> -</li> -<li><a id="org9580e4d"></a>2) λf<br /> -<div class="outline-text-6" id="text-org9580e4d"> -<p> -∀λ ∈ ℝ : λf : I –> ℝ<br /> - x –> (λf)(x) = λf (x)<br /> -</p> -</div> -</li> -<li><a id="orgc657e9e"></a>3) f*g<br /> -<div class="outline-text-6" id="text-orgc657e9e"> -<p> -(f*g): I –> ℝ<br /> - x –> (f*g)(x) = f (x) x g(x)<br /> -</p> -</div> -</li> -<li><a id="org8718fe3"></a>4) f/g<br /> -<div class="outline-text-6" id="text-org8718fe3"> -<p> -f/g : I –> ℝ<br /> - x –> f (x)/g(x) , g(x) ≠ 0<br /> -</p> -</div> -</li> -</ul> -</li> -</ul> -</div> -<div id="outline-container-org3151412" class="outline-4"> -<h4 id="org3151412">Les Limites :</h4> -<div class="outline-text-4" id="text-org3151412"> -<p> -f : I –> ℝ<br /> - x –> f (x)<br /> - x<sub>0</sub> ∈ I ; x<sub>0</sub> extrémité de l’intervalle.<br /> -</p> - -<p> -Lim<sub>x –> x<sub>0</sub></sub> f (x) est a Limite de f (x) quand x tend vers x<sub>0</sub><br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org378d0db"></a>Lim<sub>x –> x<sub>0</sub></sub> f (x) = l<br /> -<div class="outline-text-5" id="text-org378d0db"> -<p> -=> |x - x<sub>0</sub>| < ẟ , |f (x) - l| < ε<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org287d826" class="outline-4"> -<h4 id="org287d826">La continuité :</h4> -<div class="outline-text-4" id="text-org287d826"> -<p> -Soit f : I –> ℝ I = Df<br /> - x –> f (x) x<sub>0</sub> ∈ I<br /> -f est continue en x<sub>0</sub> ⇔ Lim<sub>x –> x<sub>0</sub></sub> f (x) = f (x<sub>0</sub>)<br /> -∀ε > 0 , ∃ẟ > 0 , |x - x<sub>0</sub>| < ẟ ⇒ |f (x) - f (x<sub>0</sub>)| < ε<br /> -</p> -</div> -</div> -<div id="outline-container-orgc77ab14" class="outline-4"> -<h4 id="orgc77ab14">Prolongement par continuité :</h4> -<div class="outline-text-4" id="text-orgc77ab14"> -<p> -Soit f : I/ {x<sub>0</sub>} –> ℝ<br /> - x –> f (x)<br /> -</p> - -<p> -Si lim<sub>x –> x<sub>0</sub></sub> f (x) = l Alors f est prolongéable par continuité en x<sub>0</sub><br /> -</p> - -<p> -On défini :<br /> -f~ = f (x) si x ≠ x<sub>0</sub><br /> -ET<br /> -l si x = x<sub>0</sub><br /> - f~ : I –> ℝ<br /> - x –> f (x)<br /> -</p> -</div> -</div> -<div id="outline-container-org8edfe47" class="outline-4"> -<h4 id="org8edfe47">Théorème des valeurs intermédiaires :</h4> -<div class="outline-text-4" id="text-org8edfe47"> -<p> -f : [a,b] –> ℝ<br /> -Si f est continue sur [a,b]<br /> -Alors ∀y ∈ f ([a,b]) ⇒ ∃x ∈ [a,b] ; y = f (x)<br /> -</p> - -<ol class="org-ol"> -<li>Si f est continue sur [a,b]<br /></li> -<li>Si f (a) * f (b) < 0<br /></li> -</ol> -<p> -Donc ∃ c ∈ ]a,b[ , f (c) = 0<br /> -</p> -</div> -</div> -<div id="outline-container-orgea41b1c" class="outline-4"> -<h4 id="orgea41b1c">Fonction croissante :</h4> -<div class="outline-text-4" id="text-orgea41b1c"> -<p> -f : I –> J<br /> - f est croissante si ∀ x<sub>1</sub>,x<sub>2</sub> ∈ I<br /> - x<sub>1</sub> < x<sub>2</sub> ⇒ f (x<sub>1</sub>) ≤ f (x<sub>2</sub>)<br /> -</p> - -<p> -f est strictement croissante si ∀ x<sub>1</sub>,x<sub>2</sub> ∈ I<br /> - x<sub>1</sub> < x<sub>2</sub> ⇒ f (x<sub>1</sub>) < f (x<sub>2</sub>)<br /> -</p> - -<p> -Si f est croissante ou décroissante, alors elle est bornée.<br /> -</p> -</div> -</div> -<div id="outline-container-orgd45a9b4" class="outline-4"> -<h4 id="orgd45a9b4">Injection = Strictement monotonne :</h4> -<div class="outline-text-4" id="text-orgd45a9b4"> -<p> -f : I –> J<br /> -f est injective si ∀ x<sub>1</sub>,x<sub>2</sub> ∈ I , f (x<sub>1</sub>) = f (x<sub>2</sub>) ⇒ x<sub>1</sub> = x<sub>2</sub><br /> -</p> -</div> -</div> -<div id="outline-container-org189c903" class="outline-4"> -<h4 id="org189c903">Surjection = Continuité :</h4> -<div class="outline-text-4" id="text-org189c903"> -<p> -f est surjective si ∀ y ∈ J, ∃ x ∈ I , y = f (x)<br /> -</p> -</div> -</div> -<div id="outline-container-org07713a2" class="outline-4"> -<h4 id="org07713a2">Bijection :</h4> -<div class="outline-text-4" id="text-org07713a2"> -<p> -Si f est injective et surjective, alors f est bijective<br /> -f est bijective donc elle admet une bijection réciproque<br /> -</p> -</div> -</div> -<div id="outline-container-org7512d26" class="outline-4"> -<h4 id="org7512d26">Théorème de bijection :</h4> -<div class="outline-text-4" id="text-org7512d26"> -<p> -Si f est continue et strictement monotone alors elle est bijective.<br /> -f admet une bijection réciproque f{-1}.<br /> -f{-1} a le même sens de variation que f.<br /> -</p> -</div> -</div> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2023-11-14 Tue 23:06</p> -</div> -</body> -</html> \ No newline at end of file diff --git a/uni_notes/architecture.html b/uni_notes/architecture.html deleted file mode 100755 index 290e923..0000000 --- a/uni_notes/architecture.html +++ /dev/null @@ -1,968 +0,0 @@ -<?xml version="1.0" encoding="utf-8"?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> -<head> -<!-- 2023-11-01 Wed 20:16 --> -<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> -<meta name="viewport" content="width=device-width, initial-scale=1" /> -<title>Architecture 1</title> -<meta name="author" content="Crystal" /> -<meta name="generator" content="Org Mode" /> -<link rel="stylesheet" type="text/css" href="../src/css/colors.css"/> -<link rel="stylesheet" type="text/css" href="../src/css/style.css"/> -<link rel="icon" type="image/x-icon" href="https://crystal.tilde.institute/favicon.png"> -</head> -<body> -<div id="org-div-home-and-up"> - <a accesskey="h" href="../../../uni_notes/"> UP </a> - | - <a accesskey="H" href="https://crystal.tilde.institute/"> HOME </a> -</div><div id="content" class="content"> -<h1 class="title">Architecture 1</h1> -<div id="table-of-contents" role="doc-toc"> -<h2>Table of Contents</h2> -<div id="text-table-of-contents" role="doc-toc"> -<ul> -<li><a href="#org3fa8932">Premier cours : Les systémes de numération <i>Sep 27</i> :</a> -<ul> -<li> -<ul> -<li><a href="#orgb23a1f3"><b>Examples :</b></a></li> -</ul> -</li> -<li><a href="#orga02a1f6">Comment passer d’un systéme a base 10 a un autre</a> -<ul> -<li><a href="#org8c7a5f5">Pour les chiffres entiers :</a></li> -<li><a href="#org6378ac0">Pour les chiffres non entiers :</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#org251a561">2nd cours : Les systèmes de numération (Suite) <i>Oct 3</i> :</a> -<ul> -<li><a href="#org2a38085">Comment passer d’une base N a la base 10 :</a></li> -<li><a href="#orgc0fdca1">Comment passer d’une base N a une base N^(n) :</a> -<ul> -<li><a href="#orgba624be">Exemple :</a></li> -</ul> -</li> -<li><a href="#org789d800">L’arithmétique binaire :</a> -<ul> -<li><a href="#orgac84614">L’addition :</a></li> -<li><a href="#org4829f28">La soustraction :</a></li> -</ul> -</li> -<li><a href="#org110b8dd">TP N°1 :</a> -<ul> -<li><a href="#org54d7fdf">Exo1:</a></li> -<li><a href="#org6654eb2">Exo2:</a></li> -<li><a href="#org9da39d0">Exo3:</a></li> -</ul> -</li> -<li><a href="#org2039fb1">L’arithmétique binaire (Suite): <i>Oct 4</i></a> -<ul> -<li><a href="#orgfc45d53">La multiplication :</a></li> -<li><a href="#org91fcccc">La division :</a></li> -</ul> -</li> -</ul> -</li> -<li><a href="#orgcbf8da9">4th cours : Le codage <i>Oct 10</i></a> -<ul> -<li><a href="#org34693c1">Le codage des entiers positifs</a></li> -<li><a href="#org3c8ed5c">Le codage des nombres relatifs</a> -<ul> -<li><a href="#orgb2d4951">Remarque</a></li> -<li><a href="#orgca1d761">Le codage en signe + valeur absolue (SVA):</a></li> -<li><a href="#orgd2c678f">Codage en compliment a 1 (CR):</a></li> -<li><a href="#org9961620">Codage en compliment a 2 (CV):</a></li> -</ul> -</li> -</ul> -</li> -</ul> -</div> -</div> -<div id="outline-container-org3fa8932" class="outline-2"> -<h2 id="org3fa8932">Premier cours : Les systémes de numération <i>Sep 27</i> :</h2> -<div class="outline-text-2" id="text-org3fa8932"> -<p> -Un système de numération est une méthode pour représenter des nombres à l’aide de symboles et de règles. Chaque système, comme le décimal (base 10) ou le binaire (base 2), utilise une base définie pour représenter des valeurs numériques. Il est caractérisé par 3 entitiés mathématiques importantes:<br /> -</p> - -<ol class="org-ol"> -<li>Une base (genre 10, ou 2)<br /></li> -<li>Un ensemble de chiffres<br /></li> -<li>Des régles de représentations des nombres<br /></li> -</ol> -</div> -<div id="outline-container-orgb23a1f3" class="outline-4"> -<h4 id="orgb23a1f3"><b>Examples :</b></h4> -<div class="outline-text-4" id="text-orgb23a1f3"> -<p> -<i>B10 est un systéme de numération caractérisé par:</i><br /> -</p> -<ul class="org-ul"> -<li>Base = 10<br /></li> -<li>Un ensemble de chiffres : (0,1,2,3,4,5,6,7,8,9)<br /></li> -</ul> - -<p> -<i>B16 est un autre systéme de numération caractérisé par:</i><br /> -</p> -<ul class="org-ul"> -<li>Base = 16<br /></li> -<li><p> -Un ensemble de chiffres : (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F)<br /> -</p> - -<p> -<b>Puisse-qu’on peut pas utiliser des nombres a deux chiffres, on utilise des lettres aprés 9, en leur donnant des valeurs tel que :</b><br /> -</p> - -<p> -A : 10 ; B : 11 ; C : 12 ; D : 13 ; E : 14 ; F : 15<br /> -</p></li> -</ul> -</div> -</div> -<div id="outline-container-orga02a1f6" class="outline-3"> -<h3 id="orga02a1f6">Comment passer d’un systéme a base 10 a un autre</h3> -<div class="outline-text-3" id="text-orga02a1f6"> -<p> -On symbolise un chiffre dans la base x par : (Nombre)x<br /> -</p> -</div> -<div id="outline-container-org8c7a5f5" class="outline-4"> -<h4 id="org8c7a5f5">Pour les chiffres entiers :</h4> -<div class="outline-text-4" id="text-org8c7a5f5"> -<p> -<b>On fait une division successive, on prends le nombre 3257 comme exemple, on veut le faire passer d’une base décimale á une base 16:</b><br /> -</p> - - -<p> -(3257)10 -—> (?)16<br /> -</p> - - -<p> -On dévise 3257 par 16, et les restants de la division serra la valeur en base16:<br /> -</p> - -<p> -3257/16 = 203 + <b>9</b> / 16<br /> -</p> - -<p> -203/16 = 12 + <b>B</b> / 16 <i>REMARQUE, 11 N’APPARTIENS PAS A L’ENSEMBLE DES CHIFFRES EN BASE16, CE QUI VEUT DIRE QU’ON LE REMPLACE PAR SON EQUIVALENT, DANS CE CAS LA: <b>B</b></i><br /> -</p> - -<p> -12/16 = 0 + <b>C</b> / 16 <i>Pareil ici, 12 n’existe pas, donc c’est C. Autre note : La division s’arréte quand le résultat de la division est nul</i><br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org9a466ee"></a><b>Conclusion:</b><br /> -<div class="outline-text-5" id="text-org9a466ee"> -<p> -(3257)10 -—> (CB9)16<br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org6378ac0" class="outline-4"> -<h4 id="org6378ac0">Pour les chiffres non entiers :</h4> -<div class="outline-text-4" id="text-org6378ac0"> -<p> -<b>On fait la division successive pour la partie entiére, et une multiplication successive pour la partie rationelle:</b><br /> -</p> - -<p> -(3257,32)10 -—> (?)16<br /> -</p> - -<p> -On a déja la partie entiére donc on s’occupe de la partie aprés la virgule:<br /> -</p> - -<p> -0,32 x 16 = <b>5</b>,12<br /> -</p> - -<p> -0,12 x 16 = <b>1</b>,92<br /> -</p> - -<p> -0,92 x 16 = <b>E</b>,72 <i>On a pas de 15 donc c’est un E</i><br /> -</p> - -<p> -0,72 x 16 = <b>B</b>,52<br /> -</p> - -<p> -0,52 x 16 = <b>8</b>,32<br /> -</p> - -<p> -0,32 x 16 = <b>5</b>,12<br /> -</p> - -<p> -…<br /> -</p> - -<p> -<i>On s’arréte quand on trouve un chiffre entier, et si on trouve pas, on s’arréte quand on remarque une répetition, dans ce cas la, la séquance 51EB8 vas se répéter indéfiniment, donc on se contente d’écrire la partie qui se répéte avec une barre en haut</i><br /> -</p> - - -<p> -(3257,32)10 -—> (CB9, <span class="underline">51EB8</span>)16<br /> -</p> -</div> -</div> -</div> -</div> -<div id="outline-container-org251a561" class="outline-2"> -<h2 id="org251a561">2nd cours : Les systèmes de numération (Suite) <i>Oct 3</i> :</h2> -<div class="outline-text-2" id="text-org251a561"> -</div> -<div id="outline-container-org2a38085" class="outline-3"> -<h3 id="org2a38085">Comment passer d’une base N a la base 10 :</h3> -<div class="outline-text-3" id="text-org2a38085"> -<p> -Prenons comme exemple le nombre (11210,0011)3 , chaque chiffre dans ce nombre a un rang qui commence par 0 au premier chiffre (a gauche de la virgule) et qui augmente d’un plus qu’on avance a gauche, et diminue si on part a droite. Dans ce cas la :<br /> -</p> - - -<p> -(11210,0011)3 ; le 0 est de rang 0, le 1 est de rang 1, le 2 est de rang 2, le 1 est de rang 3, le 1 est de rang 4. Et si on part du coté de la virgule, 0 est de rang -1, 0 est de rang -2, le 1 est de rang -3, et le 1 est de rang -4.<br /> -</p> - - -<p> -Et pour passer a la base 10, il suffit d’appliquer cette formule : <b>Chiffre x Base^(rang) + 2emeChiffre x Base^(rang)… etc</b>, donc dans notre example:<br /> -</p> - - -<p> -<i>0 x 3° + 1 x 3¹ + 2 x 3² + 1 x 3³ + 1 x 3^4 + 0 x 3¯¹ + 0 x 3¯² + 1 x 3¯³ + 1 x 3^(-4) ≈ (129,05)10</i><br /> -</p> -</div> -</div> -<div id="outline-container-orgc0fdca1" class="outline-3"> -<h3 id="orgc0fdca1">Comment passer d’une base N a une base N^(n) :</h3> -<div class="outline-text-3" id="text-orgc0fdca1"> -<p> -Si il ya une relation entre une base et une autre, on peut directement transformer vers cette base.<br /> -</p> -</div> -<div id="outline-container-orgba624be" class="outline-4"> -<h4 id="orgba624be">Exemple :</h4> -<div class="outline-text-4" id="text-orgba624be"> -<p> -Pour passer de la base 2 a la base 8 (8 qui est 2³) on découpe les chiffres 3 par 3<br /> -</p> - - -<p> -(1 101 011, 011)2 ; Pour le dernier 1 qui est seul <code>tout comme moi</code> il suffit d’ajouter des 0 à gauche (car on peut) pour compléter le découpage.<br /> -</p> - - -<p> -(001 101 011, 011)2; Next step c’est de dessiner le tableau de conversion de la base 2 a la base 8 ( un tableau a 3 bits )<br /> -</p> - - -<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> - - -<colgroup> -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> - -<col class="org-right" /> -</colgroup> -<thead> -<tr> -<th scope="col" class="org-right">N</th> -<th scope="col" class="org-right"> </th> -<th scope="col" class="org-right"> </th> -<th scope="col" class="org-right"> </th> -</tr> -</thead> -<tbody> -<tr> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -</tr> - -<tr> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">2</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -</tr> - -<tr> -<td class="org-right">3</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">4</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">0</td> -</tr> - -<tr> -<td class="org-right">5</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -<td class="org-right">1</td> -</tr> - -<tr> -<td class="org-right">6</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">0</td> -</tr> - -<tr> -<td class="org-right">7</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -<td class="org-right">1</td> -</tr> -</tbody> -</table> - - -<p> -Pour remplir on a qu’a diviser les chiffres en deux, et mettre des 0 dans la première partie et des 1 dans la 2éme, et en faire de même pour les autres colonnes .<br /> -</p> - - -<p> -Maintenant il suffit de trouver l’équivalent de la base2 en base8 :<br /> -</p> - - -<p> -001 c’est 1 ; 101 c’est 5 ; 011 c’est 3 ; donc <b>(1101011,011)2 —> (153,3)8</b><br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org789d800" class="outline-3"> -<h3 id="org789d800">L’arithmétique binaire :</h3> -<div class="outline-text-3" id="text-org789d800"> -</div> -<div id="outline-container-orgac84614" class="outline-4"> -<h4 id="orgac84614">L’addition :</h4> -<div class="outline-text-4" id="text-orgac84614"> -<p> -0 + 0 = 0 On retiens 0<br /> -</p> - - -<p> -1 + 0 = 1 On retiens 0<br /> -</p> - - -<p> -0 + 1 = 1 On retiens 0<br /> -</p> - - -<p> -1 + 1 = 0 On retiens 1<br /> -</p> - - -<p> -1 + 1 + 1 = 1 On retiens 1<br /> -</p> - - -<p> -Donc 0110 + 1101 = 10011<br /> -</p> -</div> -</div> -<div id="outline-container-org4829f28" class="outline-4"> -<h4 id="org4829f28">La soustraction :</h4> -<div class="outline-text-4" id="text-org4829f28"> -<p> -0 - 0 = 0 On emprunt = 0<br /> -</p> - - -<p> -1 - 0 = 1 On emprunt = 0<br /> -</p> - - -<p> -0 - 1 = 1 On emprunt = 1<br /> -</p> - - -<p> -1 - 1 = 0 On emprunt = 0<br /> -</p> -</div> -</div> -</div> -<div id="outline-container-org110b8dd" class="outline-3"> -<h3 id="org110b8dd">TP N°1 :</h3> -<div class="outline-text-3" id="text-org110b8dd"> -</div> -<div id="outline-container-org54d7fdf" class="outline-4"> -<h4 id="org54d7fdf">Exo1:</h4> -<div class="outline-text-4" id="text-org54d7fdf"> -<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> - - -<colgroup> -<col class="org-left" /> - -<col class="org-left" /> - -<col class="org-left" /> - -<col class="org-left" /> - -<col class="org-left" /> -</colgroup> -<thead> -<tr> -<th scope="col" class="org-left">Base 10</th> -<th scope="col" class="org-left">Base 2</th> -<th scope="col" class="org-left">Base 3</th> -<th scope="col" class="org-left">Base 8</th> -<th scope="col" class="org-left">Base 16</th> -</tr> -</thead> -<tbody> -<tr> -<td class="org-left">22,75</td> -<td class="org-left">10110,11</td> -<td class="org-left">211, <span class="underline">20</span></td> -<td class="org-left">26,6</td> -<td class="org-left">F6,C</td> -</tr> - -<tr> -<td class="org-left">684,125</td> -<td class="org-left">1010101100,001</td> -<td class="org-left">221100, <span class="underline">01</span></td> -<td class="org-left">1254,1</td> -<td class="org-left">2AC,2</td> -</tr> - -<tr> -<td class="org-left">3931,625</td> -<td class="org-left">111101011011,101</td> -<td class="org-left">1101121, <span class="underline">12</span></td> -<td class="org-left">7533,5</td> -<td class="org-left">F5B,A</td> -</tr> - -<tr> -<td class="org-left">52,38</td> -<td class="org-left">110100,011</td> -<td class="org-left">1221,101</td> -<td class="org-left">64,3</td> -<td class="org-left">34,6147</td> -</tr> - -<tr> -<td class="org-left">10,67</td> -<td class="org-left">1010,101</td> -<td class="org-left">23,5</td> -<td class="org-left">12,5</td> -<td class="org-left">A,AB85</td> -</tr> -</tbody> -</table> -</div> -<ul class="org-ul"> -<li><a id="orga7c42ee"></a>(10110,11)2<br /> -<div class="outline-text-5" id="text-orga7c42ee"> -<p> -0 x 2° + 1 x 2¹ + 1 x 2² + 0 x 2³ + 1 x 2^(4) + 1 x 2¯¹ + 1 x 2¯² = (22.75)10<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org02d1304"></a>(22,75)10 -—> (3)<br /> -<div class="outline-text-6" id="text-org02d1304"> -<p> -22/3 = 7 R <b>1</b> ; 7/3 = 2 R <b>1</b> ; 2/3 = 0 R <b>2</b><br /> -</p> - - -<p> -0,75 x 3 = <b>2</b>.25 ; 0,25 x 3 = <b>0</b>.75 …..<br /> -</p> - - -<p> -(22,75)10 -—> (211, <span class="underline">20</span>)<br /> -</p> -</div> -</li> -<li><a id="org00a17b7"></a>(10110,11)2 -—> (8)<br /> -<div class="outline-text-6" id="text-org00a17b7"> -<p> -8 = 2³ ; (010 110,110)2 -—> (?)8<br /> -</p> - - -<p> -En utilisant le tableau 3bits :<br /> -</p> - - -<p> -010 : 2 ; 110 : 6 ; 110 : 6<br /> -</p> - - -<p> -(10110,11)2 -—> (26,6)8<br /> -</p> -</div> -</li> -<li><a id="org8bffc7b"></a>(22,75)10 -—> (16)<br /> -<div class="outline-text-6" id="text-org8bffc7b"> -<p> -22/16 = 1 R <b>6</b> ; 1/16 : 0 R <b>F</b><br /> -</p> - - -<p> -0,75 x 16 = <b>C</b><br /> -</p> - - -<p> -(22,75)10 -—> (F6,C)16<br /> -</p> -</div> -</li> -</ul> -</li> -<li><a id="orgd6d1187"></a>(1254,1)8<br /> -<div class="outline-text-5" id="text-orgd6d1187"> -<p> -4 x 8° + 5 x 8¹ + 2 x 8² + 1 x 8³ + 1 x 8¯¹ = (684,125)10<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orgfe79941"></a>(1254,1)8 -—> (?)2<br /> -<div class="outline-text-6" id="text-orgfe79941"> -<p> -En utilisant le tableau 3bits :<br /> -</p> - - -<p> -001 010 101 100,001 <i>We will get rid of the leading zeros</i><br /> -</p> - - -<p> -(1010101100,001)2<br /> -</p> -</div> -</li> -<li><a id="org5468c02"></a>(684,125)10 -—> (?)3<br /> -<div class="outline-text-6" id="text-org5468c02"> -<p> -684/3 = 228 R <b>0</b> ; 228/3 = 76 R <b>0</b> ; 76/3 = 25 R <b>1</b> ; 25/3 = 8 R <b>1</b> ; 8/3 = 2 R <b>2</b> ; 2/3 = 0 R <b>2</b><br /> -</p> - - -<p> -0,125 x 3 = <b>0</b>,375 ; 0,375 x 3 = <b>1</b>,125<br /> -</p> - - -<p> -(221100, <span class="underline">01</span>)3<br /> -</p> -</div> -</li> -<li><a id="org8acf355"></a>(684,125)10 -—> (?)16<br /> -<div class="outline-text-6" id="text-org8acf355"> -<p> -684/16 = 42 R <b>C</b> ; 42/16 = 2 R <b>A</b> ; 2/16 0 R <b>2</b><br /> -</p> - - -<p> -0,125 x 16 = <b>2</b><br /> -</p> - - -<p> -(2AC,2)16<br /> -</p> -</div> -</li> -</ul> -</li> -<li><a id="orgaed5ea2"></a>(F5B,A)16<br /> -<div class="outline-text-5" id="text-orgaed5ea2"> -<p> -11 x 16° + 5 x 16 + 15 x 16² + 10 x 16¯¹ = (3931,625)10<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org56c0052"></a>(3931,625)10 -—> (8)<br /> -<div class="outline-text-6" id="text-org56c0052"> -<p> -3931/8 = 491 R <b>3</b> ; 491/8 = 61 R <b>3</b> ; 61/8 = 7 R <b>5</b> ; 7/8 = 0 R <b>7</b><br /> -</p> - - -<p> -0,625 x 8 = <b>5</b><br /> -</p> - - -<p> -(7533,5)8<br /> -</p> -</div> -</li> -<li><a id="org64e9962"></a>(7533,5)8 -—> (2)<br /> -<div class="outline-text-6" id="text-org64e9962"> -<p> -En utilisant le tableau 3bits<br /> -</p> - -<p> -(111 101 011 011,101)2<br /> -</p> -</div> -</li> -<li><a id="org2850a22"></a>(3931,625)10 -—> (3)<br /> -<div class="outline-text-6" id="text-org2850a22"> -<p> -3931/3 = 1310 R <b>1</b> ; 1310/3 = 436 R <b>2</b> ; 436/3 = 145 R <b>1</b> ; 145/3 = 48 R <b>1</b> ; 48/3 = 16 R <b>0</b> ; 16/3 = 5 R <b>1</b> ; 5/3 = 1 R <b>2</b> ; 1/3 = 0 R <b>1</b><br /> -</p> - - -<p> -0.625 x 3 = <b>1</b>,875 ; 0,875 x 3 = <b>2</b>,625<br /> -</p> - - -<p> -(1101121, <span class="underline">12</span>)3<br /> -</p> -</div> -</li> -</ul> -</li> -<li><a id="org2ee5d93"></a>(52,38)10<br /> -<div class="outline-text-5" id="text-org2ee5d93"> -<p> -52/2 = 26 R <b>0</b> ; 26/2 = 13 R <b>0</b> ; 13/2 = 6 R <b>1</b> ; 6/2 = 3 R <b>0</b> ; 3/2 = 1 R <b>1</b> ; 1/2 = 0 R <b>1</b><br /> -</p> - - -<p> -0,38 x 2 = <b>0</b>,76 ; 0,76 x 2 = <b>1</b>,52 ; 0,52 x 2 = <b>1</b>,04 ; 0,04 x 2 = <b>0</b>,08 ….<br /> -</p> - - -<p> -(110100,0110)2<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="org3f89d6a"></a>(52,38)10 -—> (3)<br /> -<div class="outline-text-6" id="text-org3f89d6a"> -<p> -52/3 = 17 R <b>1</b> ; 17/3 = 5 R <b>2</b> ; 5/3 = 1 R <b>2</b> ; 1/3 = 0 R <b>1</b><br /> -</p> - - -<p> -0,38 x 3 = <b>1</b>.14 ; 0,14 x 3 = <b>0</b>.42 ; 0,42 x 3 = <b>1</b>.26 ; 0.26 x 3 = <b>0</b>.78 …<br /> -</p> - - -<p> -(1221,101)3<br /> -</p> -</div> -</li> -<li><a id="org388e3c0"></a>(110100,011)2 -—> (8)<br /> -<div class="outline-text-6" id="text-org388e3c0"> -<p> -En utilisant le tableau 3bits:<br /> -</p> - - -<p> -(110 100,011)2 -—> (64,3)8<br /> -</p> -</div> -</li> -<li><a id="orgb909e73"></a>(52,38)10 -—> (16)<br /> -<div class="outline-text-6" id="text-orgb909e73"> -<p> -52/16 = 3 R <b>4</b> ; 3/16 = 0 R <b>3</b><br /> -</p> - - -<p> -0,38 x 16 = <b>6</b>,08 ; 0,08 x 16 = <b>1</b>,28 ; 0,28 x 16 = <b>4</b>,48 ; 0,48 x 16 = <b>7</b>,68 ….<br /> -</p> - - -<p> -(34,6147)16<br /> -</p> -</div> -</li> -</ul> -</li> -<li><a id="org75b2f51"></a>(23,5)3<br /> -<div class="outline-text-5" id="text-org75b2f51"> -<p> -3 x 3° + 2 x 3 + 5 x 3¯¹ = (10.67)10<br /> -</p> -</div> -<ul class="org-ul"> -<li><a id="orgbc5bb6a"></a>(10,67)10 -—> (2)<br /> -<div class="outline-text-6" id="text-orgbc5bb6a"> -<p> -10/2 = 5 R <b>0</b> ; 5/2 = 2 R <b>1</b> ; 2/2 = 1 R <b>0</b> ; 1/2 = 0 R <b>1</b><br /> -</p> - - -<p> -0,67 x 2 = <b>1</b>,34 ; 0,34 x 2 = <b>0</b>,68 ; 0,68 x 2 = <b>1</b>,36 ; 0,36 x 2 = <b>0</b>,72 …<br /> -</p> - - -<p> -(1010,101)2<br /> -</p> -</div> -</li> -<li><a id="org0edf1dd"></a>(001 010,101)2 -—> (8)<br /> -<div class="outline-text-6" id="text-org0edf1dd"> -<p> -<b>Ô Magic 3bits table, save me soul, me children and me maiden:</b><br /> -</p> - - -<p> -(12,5)8<br /> -</p> -</div> -</li> -<li><a id="org58aafdf"></a>(10,67)10 -—> (16)<br /> -<div class="outline-text-6" id="text-org58aafdf"> -<p> -10/16 = 0 R <b>A</b><br /> -</p> - - -<p> -0,67 x 16 = <b>A</b>,72 ; 0,72 x 16 = <b>B</b>,52 ; 0,52 x 16 = <b>8</b>,32 ; 0,32 x 16 = <b>5</b>,12 …<br /> -</p> - - -<p> -(A,AB85)16<br /> -</p> -</div> -</li> -</ul> -</li> -</ul> -</div> -<div id="outline-container-org6654eb2" class="outline-4"> -<h4 id="org6654eb2">Exo2:</h4> -<div class="outline-text-4" id="text-org6654eb2"> -</div> -<ul class="org-ul"> -<li><a id="org15754eb"></a>(34)? = (22)10<br /> -<div class="outline-text-5" id="text-org15754eb"> -<p> -(34)a = (22)10 ; 4 x a° + 3 x a = 22 ; 4 + 3a = 22 ; 3a = 18<br /> -</p> - - -<p> -<b>a = 6</b><br /> -</p> -</div> -</li> -<li><a id="org1c4cbd0"></a>(75)? = (117)10<br /> -<div class="outline-text-5" id="text-org1c4cbd0"> -<p> -(75)b = (117)10 ; 5 x b° + 7 x b¹ = 117 ; 5 + 7b = 117 ; 7b = 112<br /> -</p> - - -<p> -<b>b = 16</b><br /> -</p> -</div> -</li> -</ul> -</div> -<div id="outline-container-org9da39d0" class="outline-4"> -<h4 id="org9da39d0">Exo3:</h4> -<div class="outline-text-4" id="text-org9da39d0"> -</div> -<ul class="org-ul"> -<li><a id="org9098512"></a>(101011)2 + (111011)2<br /> -<div class="outline-text-5" id="text-org9098512"> -<p> -101011 + 111011 = 1100110<br /> -</p> -</div> -</li> -<li><a id="org390626e"></a>(1011,1101)2 + (11,1)2<br /> -<div class="outline-text-5" id="text-org390626e"> -<p> -1011,1101 + 11,1000 = 1111,0101<br /> -</p> -</div> -</li> -<li><a id="org3d08c66"></a>(1010,0101)2 - (110,1001)2<br /> -<div class="outline-text-5" id="text-org3d08c66"> -<p> -1010,0101 - 110,1001 = 11,1100<br /> -</p> -</div> -</li> -</ul> -</div> -</div> -<div id="outline-container-org2039fb1" class="outline-3"> -<h3 id="org2039fb1">L’arithmétique binaire (Suite): <i>Oct 4</i></h3> -<div class="outline-text-3" id="text-org2039fb1"> -</div> -<div id="outline-container-orgfc45d53" class="outline-4"> -<h4 id="orgfc45d53">La multiplication :</h4> -<div class="outline-text-4" id="text-orgfc45d53"> -<p> -0 x 0 = 0<br /> -</p> - - -<p> -0 x 1 = 0<br /> -</p> - - -<p> -1 x 0 = 0<br /> -</p> - - -<p> -1 x 1 = 1<br /> -</p> -</div> -</div> -<div id="outline-container-org91fcccc" class="outline-4"> -<h4 id="org91fcccc">La division :</h4> -<div class="outline-text-4" id="text-org91fcccc"> -<p> -On divise de la manière la plus normale du monde !!!<br /> -</p> -</div> -</div> -</div> -</div> -<div id="outline-container-orgcbf8da9" class="outline-2"> -<h2 id="orgcbf8da9">4th cours : Le codage <i>Oct 10</i></h2> -<div class="outline-text-2" id="text-orgcbf8da9"> -</div> -<div id="outline-container-org34693c1" class="outline-3"> -<h3 id="org34693c1">Le codage des entiers positifs</h3> -<div class="outline-text-3" id="text-org34693c1"> -<p> -Le codage sur n bits permet de representer tout les entiers naturels compris entre [0, 2^n - 1]. On peut coder sur 8bits les entiers entre [0;2^8 - 1(255)]<br /> -</p> -</div> -</div> -<div id="outline-container-org3c8ed5c" class="outline-3"> -<h3 id="org3c8ed5c">Le codage des nombres relatifs</h3> -<div class="outline-text-3" id="text-org3c8ed5c"> -</div> -<div id="outline-container-orgb2d4951" class="outline-4"> -<h4 id="orgb2d4951">Remarque</h4> -<div class="outline-text-4" id="text-orgb2d4951"> -<p> -Quelque soit le codage utilise, par convention le dernier bit est reserve pour le signe. ou 1 est negatif et 0 est positif.<br /> -</p> -</div> -</div> -<div id="outline-container-orgca1d761" class="outline-4"> -<h4 id="orgca1d761">Le codage en signe + valeur absolue (SVA):</h4> -<div class="outline-text-4" id="text-orgca1d761"> -<p> -Avec n bits le n eme est reserve au signe : [-(2^n-1)-1 , 2^n-1 -1]. Sur 8bits [-127, 127]<br /> -</p> -</div> -</div> -<div id="outline-container-orgd2c678f" class="outline-4"> -<h4 id="orgd2c678f">Codage en compliment a 1 (CR):</h4> -<div class="outline-text-4" id="text-orgd2c678f"> -<p> -On obtiens le compliment a 1 d’un nombre binaire en inversant chaqu’un de ses bits (1 -> 0 et 0-> 1) les nombres positifs sont la meme que SVA (il reste tel qu’il est)<br /> -</p> -</div> -</div> -<div id="outline-container-org9961620" class="outline-4"> -<h4 id="org9961620">Codage en compliment a 2 (CV):</h4> -<div class="outline-text-4" id="text-org9961620"> -<p> -C’est literallement CR + 1 pour les negatifs et SVA pour les nombres positifs<br /> -</p> -</div> -</div> -</div> -</div> -</div> -<div id="postamble" class="status"> -<p class="author">Author: Crystal</p> -<p class="date">Created: 2023-11-01 Wed 20:16</p> -</div> -</body> -</html> \ No newline at end of file |