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Signed-off-by: Abdulkadir Furkan Şanlı <abdulocracy@disroot.org>
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Abdulkadir Furkan Şanlı 2019-12-17 16:32:27 +01:00
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public/about/index.html
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<meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta http-equiv="content-type" content="text/html; charset=utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1">
<meta name="description" content=" name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy "/> <meta name="description" content=" name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy "/>
<meta name="keywords" content=""/> <meta name="keywords" content=""/>
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<link rel="canonical" href="https://abdulocra.cy/about/" /> <link rel="canonical" href="https://abdulocra.cy/about/" />
@ -29,7 +29,7 @@
<meta name="twitter:card" content="summary" /> <meta name="twitter:card" content="summary" />
<meta name="twitter:title" content="about :: abdulocracy&#39;s personal site — " /> <meta name="twitter:title" content="about :: abdulocracy&#39;s personal site — " />
<meta name="twitter:description" content=" name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy " /> <meta name="twitter:description" content=" name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy " />
<meta name="twitter:site" content="https://abdulocra.cy/" /> <meta name="twitter:site" content="https://abdulocra.cy/" />
<meta name="twitter:creator" content="" /> <meta name="twitter:creator" content="" />
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<meta property="og:locale" content="en" /> <meta property="og:locale" content="en" />
<meta property="og:type" content="article" /> <meta property="og:type" content="article" />
<meta property="og:title" content="about :: abdulocracy&#39;s personal site — "> <meta property="og:title" content="about :: abdulocracy&#39;s personal site — ">
<meta property="og:description" content=" name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy " /> <meta property="og:description" content=" name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy " />
<meta property="og:url" content="https://abdulocra.cy/about/" /> <meta property="og:url" content="https://abdulocra.cy/about/" />
<meta property="og:site_name" content="about" /> <meta property="og:site_name" content="about" />
<meta property="og:image" content=""> <meta property="og:image" content="">
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<div class="post-content"> <div class="post-content">
<p><image src="face.jpg" width="173" height="150" /></p> <p><!-- raw HTML omitted --></p>
<ul> <ul>
<li>name: Abdulkadir Furkan Şanlı</li> <li>name: Abdulkadir Furkan Şanlı</li>
<li>handle: abdulocracy</li> <li>handle: abdulocracy</li>
<li>contact: <li>contact:
<ul> <ul>
<li>email: my handle at disroot dot org</li> <li>email: my handle at disroot dot org</li>
<li>irc (freenode): abdulocracy</li> <li>irc (freenode): abdulocracy</li>
</ul></li> </ul>
</li>
</ul> </ul>
</div> </div>

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<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<meta name="generator" content="Hugo 0.59.1" /> <meta name="generator" content="Hugo 0.61.0" />
<title>abdulocracy&#39;s personal site</title> <title>abdulocracy&#39;s personal site</title>
@ -167,7 +167,10 @@
<div class="post-content"> <div class="post-content">
Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. (2=7) statement (x=5) not a statement In logic we do not use the equals sign, we use the equivalence sign (\equiv). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false.
We should avoid variables when forming statements, as they may change the logical value.
(2=7) statement (x=5) not a statement In logic we do not use the equals sign, we use the equivalence sign (\equiv).
Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.
</div> </div>

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<pubDate>Wed, 20 Nov 2019 00:00:00 +0000</pubDate> <pubDate>Wed, 20 Nov 2019 00:00:00 +0000</pubDate>
<guid>https://abdulocra.cy/posts/eidma/</guid> <guid>https://abdulocra.cy/posts/eidma/</guid>
<description>Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. \(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.</description> <description>Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false.
We should avoid variables when forming statements, as they may change the logical value.
\(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\).
Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.</description>
</item> </item>
<item> <item>
@ -27,7 +30,7 @@
<pubDate>Mon, 04 Nov 2019 00:00:00 +0000</pubDate> <pubDate>Mon, 04 Nov 2019 00:00:00 +0000</pubDate>
<guid>https://abdulocra.cy/about/</guid> <guid>https://abdulocra.cy/about/</guid>
<description> name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy </description> <description> name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy </description>
</item> </item>
</channel> </channel>

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<meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta http-equiv="content-type" content="text/html; charset=utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1">
<meta name="description" content="Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. \(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc."/> <meta name="description" content="Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false.
We should avoid variables when forming statements, as they may change the logical value.
\(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\).
Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc."/>
<meta name="keywords" content=""/> <meta name="keywords" content=""/>
<meta name="robots" content="noodp"/> <meta name="robots" content="noodp"/>
<link rel="canonical" href="https://abdulocra.cy/posts/eidma/" /> <link rel="canonical" href="https://abdulocra.cy/posts/eidma/" />
@ -29,7 +32,10 @@
<meta name="twitter:card" content="summary" /> <meta name="twitter:card" content="summary" />
<meta name="twitter:title" content="Introduction to Discrete Mathematics :: abdulocracy&#39;s personal site — " /> <meta name="twitter:title" content="Introduction to Discrete Mathematics :: abdulocracy&#39;s personal site — " />
<meta name="twitter:description" content="Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. \(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc." /> <meta name="twitter:description" content="Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false.
We should avoid variables when forming statements, as they may change the logical value.
\(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\).
Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc." />
<meta name="twitter:site" content="https://abdulocra.cy/" /> <meta name="twitter:site" content="https://abdulocra.cy/" />
<meta name="twitter:creator" content="" /> <meta name="twitter:creator" content="" />
<meta name="twitter:image" content=""> <meta name="twitter:image" content="">
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<meta property="og:locale" content="en" /> <meta property="og:locale" content="en" />
<meta property="og:type" content="article" /> <meta property="og:type" content="article" />
<meta property="og:title" content="Introduction to Discrete Mathematics :: abdulocracy&#39;s personal site — "> <meta property="og:title" content="Introduction to Discrete Mathematics :: abdulocracy&#39;s personal site — ">
<meta property="og:description" content="Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. \(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc." /> <meta property="og:description" content="Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false.
We should avoid variables when forming statements, as they may change the logical value.
\(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\).
Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc." />
<meta property="og:url" content="https://abdulocra.cy/posts/eidma/" /> <meta property="og:url" content="https://abdulocra.cy/posts/eidma/" />
<meta property="og:site_name" content="Introduction to Discrete Mathematics" /> <meta property="og:site_name" content="Introduction to Discrete Mathematics" />
<meta property="og:image" content=""> <meta property="og:image" content="">
@ -158,19 +167,19 @@
</ul> </ul>
<h2 id="propositional-calculus">Propositional calculus</h2> <h2 id="propositional-calculus">Propositional calculus</h2>
<ul> <ul>
<li>Comes from the linguistic concept that things can be either true or false.</li> <li><p>Comes from the linguistic concept that things can be either true or false.</p></li>
<li>We should avoid variables when forming statements, as they may change the logical value. <li><p>We should avoid variables when forming statements, as they may change the logical value.</p>
<ul> <ul>
<li><span class="math inline">\(2=7\)</span> statement</li> <li><span class="math inline">\(2=7\)</span> statement</li>
<li><span class="math inline">\(x=5\)</span> not a statement</li> <li><span class="math inline">\(x=5\)</span> not a statement</li>
</ul></li> </ul></li>
<li>In logic we do not use the equals sign, we use the equivalence sign <span class="math inline">\(\equiv\)</span>.</li> <li><p>In logic we do not use the equals sign, we use the equivalence sign <span class="math inline">\(\equiv\)</span>.</p></li>
<li>Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.).</li> <li><p>Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.).</p></li>
<li>When doing logic, we use propositional variables (e.g. p, q, r). <li><p>When doing logic, we use propositional variables (e.g. p, q, r).</p>
<ul> <ul>
<li>Can be either <strong>true</strong> or <strong>false</strong>.</li> <li>Can be either <strong>true</strong> or <strong>false</strong>.</li>
</ul></li> </ul></li>
<li>The operations done on propositional variables are called propositional connectives. <li><p>The operations done on propositional variables are called propositional connectives.</p>
<ul> <ul>
<li>Conjunction: <span class="math inline">\(p \land q\)</span> is only true if both p and q are true <span class="math inline">\((0001)\)</span></li> <li>Conjunction: <span class="math inline">\(p \land q\)</span> is only true if both p and q are true <span class="math inline">\((0001)\)</span></li>
<li>Disjunction: <span class="math inline">\(p \lor q\)</span> is only false if both p and q are false <span class="math inline">\((0111)\)</span></li> <li>Disjunction: <span class="math inline">\(p \lor q\)</span> is only false if both p and q are false <span class="math inline">\((0111)\)</span></li>
@ -179,11 +188,11 @@
<li><span class="math inline">\(\equiv \neg p \lor q\)</span></li> <li><span class="math inline">\(\equiv \neg p \lor q\)</span></li>
</ul></li> </ul></li>
</ul></li> </ul></li>
<li>Not necessarily connectives but unary operations: <li><p>Not necessarily connectives but unary operations:</p>
<ul> <ul>
<li>Negation: Denoted by ~, <span class="math inline">\(\neg\)</span> or NOT, negates the one input <span class="math inline">\((10)\)</span>.</li> <li>Negation: Denoted by ~, <span class="math inline">\(\neg\)</span> or NOT, negates the one input <span class="math inline">\((10)\)</span>.</li>
</ul></li> </ul></li>
<li>A (propositional) formula is a “properly constructed” logical expression. <li><p>A (propositional) formula is a “properly constructed” logical expression.</p>
<ul> <ul>
<li>e.g. <span class="math inline">\(\neg[(p \lor q)] \land r\)</span></li> <li>e.g. <span class="math inline">\(\neg[(p \lor q)] \land r\)</span></li>
<li><span class="math inline">\((p \land)\)</span> is not a formula, as <span class="math inline">\(\land\)</span> requires 2 variables.</li> <li><span class="math inline">\((p \land)\)</span> is not a formula, as <span class="math inline">\(\land\)</span> requires 2 variables.</li>
@ -196,10 +205,10 @@
<li><span class="math inline">\(\neg(B \lor C)\)</span> can be written as <span class="math inline">\(\neg B \land \neg C\)</span></li> <li><span class="math inline">\(\neg(B \lor C)\)</span> can be written as <span class="math inline">\(\neg B \land \neg C\)</span></li>
</ul></li> </ul></li>
</ul></li> </ul></li>
<li>Double negation law: <span class="math inline">\(\neg(\neg p) \equiv p\)</span></li> <li><p>Double negation law: <span class="math inline">\(\neg(\neg p) \equiv p\)</span></p></li>
<li><p>De Morgan’s laws: <span class="math inline">\(\neg(p \land q) \equiv \neg p \lor \neg q\)</span> and <span class="math inline">\(\neg(p \lor q) \equiv \neg p \land \neg q\)</span>.</p></li> <li><p>De Morgan’s laws: <span class="math inline">\(\neg(p \land q) \equiv \neg p \lor \neg q\)</span> and <span class="math inline">\(\neg(p \lor q) \equiv \neg p \land \neg q\)</span>.</p></li>
<li>If and only if (<em>iff</em>): <span class="math inline">\(p \iff p \equiv (p \implies q) \land (q \implies p)\)</span></li> <li><p>If and only if (<em>iff</em>): <span class="math inline">\(p \iff p \equiv (p \implies q) \land (q \implies p)\)</span></p></li>
<li>Contraposition law: <li><p>Contraposition law:</p>
<ul> <ul>
<li><span class="math inline">\((p \implies q) \equiv (\neg q \implies \neg p)\)</span> prove by contraposition <li><span class="math inline">\((p \implies q) \equiv (\neg q \implies \neg p)\)</span> prove by contraposition
<ul> <ul>
@ -207,7 +216,7 @@
<li><span class="math inline">\((\neg q \implies \neg p) \equiv (\neg (\neg q) \lor (\neg p) \equiv (q \lor \neg p) \equiv (\neg p \lor q)\)</span></li> <li><span class="math inline">\((\neg q \implies \neg p) \equiv (\neg (\neg q) \lor (\neg p) \equiv (q \lor \neg p) \equiv (\neg p \lor q)\)</span></li>
</ul></li> </ul></li>
</ul></li> </ul></li>
<li>Contradiction law: <li><p>Contradiction law:</p>
<ul> <ul>
<li><span class="math inline">\(p \lor \neg p \equiv 1\)</span> and <span class="math inline">\(p \land \neg p \equiv 0\)</span></li> <li><span class="math inline">\(p \lor \neg p \equiv 1\)</span> and <span class="math inline">\(p \land \neg p \equiv 0\)</span></li>
</ul></li> </ul></li>

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<div class="post-content"> <div class="post-content">
Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. (2=7) statement (x=5) not a statement In logic we do not use the equals sign, we use the equivalence sign (\equiv). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false.
We should avoid variables when forming statements, as they may change the logical value.
(2=7) statement (x=5) not a statement In logic we do not use the equals sign, we use the equivalence sign (\equiv).
Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.
</div> </div>

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<pubDate>Wed, 20 Nov 2019 00:00:00 +0000</pubDate> <pubDate>Wed, 20 Nov 2019 00:00:00 +0000</pubDate>
<guid>https://abdulocra.cy/posts/eidma/</guid> <guid>https://abdulocra.cy/posts/eidma/</guid>
<description>Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. \(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.</description> <description>Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false.
We should avoid variables when forming statements, as they may change the logical value.
\(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\).
Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.</description>
</item> </item>
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5
public/tags/university-notes/index.html
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<div class="post-content"> <div class="post-content">
Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. (2=7) statement (x=5) not a statement In logic we do not use the equals sign, we use the equivalence sign (\equiv). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false.
We should avoid variables when forming statements, as they may change the logical value.
(2=7) statement (x=5) not a statement In logic we do not use the equals sign, we use the equivalence sign (\equiv).
Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.
</div> </div>

5
public/tags/university-notes/index.xml
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@ -18,7 +18,10 @@
<pubDate>Wed, 20 Nov 2019 00:00:00 +0000</pubDate> <pubDate>Wed, 20 Nov 2019 00:00:00 +0000</pubDate>
<guid>https://abdulocra.cy/posts/eidma/</guid> <guid>https://abdulocra.cy/posts/eidma/</guid>
<description>Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. \(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.</description> <description>Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false.
We should avoid variables when forming statements, as they may change the logical value.
\(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\).
Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.</description>
</item> </item>
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