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Update eidma

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Signed-off-by: Abdulkadir Furkan Şanlı <abdulkadirfsanli@protonmail.com>
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Abdulkadir Furkan Şanlı
2019-11-20 11:07:13 +01:00
parent 6744f6ffc1
commit e6290c0bd2
10 changed files with 94 additions and 61 deletions
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\(2=7\) 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:creator" content="Abdulkadir" />
<meta name="twitter:creator" content="" />
<meta name="twitter:image" content="">
@ -51,7 +51,7 @@
<meta property="og:image:width" content="2048">
<meta property="og:image:height" content="1024">
<meta property="article:published_time" content="2019-11-04 00:00:00 &#43;0000 UTC" />
<meta property="article:published_time" content="2019-11-20 00:00:00 &#43;0000 UTC" />
@ -134,14 +134,10 @@
<div class="post-meta">
<span class="post-date">
2019-11-04
2019-11-20
</span>
<span class="post-author">::
Abdulkadir
</span>
</div>
@ -431,9 +427,36 @@
<ul>
<li><span class="math">\(\phi(1)\)</span></li>
<li><span class="math">\((\forall n \geq 1) (\phi(n) \implies \phi(n+1)\)</span></li>
<li><span class="math">\((\forall n \geq 1) \phi(n) \implies \phi(n+1)\)</span></li>
<li><span class="math">\((\forall k \geq 1) \phi(k)\)</span></li>
</ul></li>
</ul>
<h2 id="functions">Functions</h2>
<ul>
<li><span class="math">\(f: \mathbb X \to \mathbb Y\)</span></li>
<li><p>Def: <span class="math">\(f \subseteq \mathbb X \times \mathbb Y\)</span> is said to be a function if:</p>
<ul>
<li><span class="math">\((\forall x \in \mathbb X)(\exists y \in \mathbb Y) (x, y) \in f(y = f(x))\)</span></li>
<li><span class="math">\((\forall a \in \mathbb X)(\forall p, q \in \mathbb Y)((a, p) \in f \land (a, q) \in f \implies p = q)\)</span></li>
</ul></li>
<li><p>Types of functions <span class="math">\(f: \mathbb X \to \mathbb Y\)</span>:</p>
<ul>
<li><span class="math">\(f\)</span> is said to be an injection ( 1 to 1 function) iff <span class="math">\((\forall x_1, x_2 \in \mathbb X) x_1 \neq x_2 \implies f(x_1) \neq f(x_2)\)</span></li>
<li><span class="math">\(f\)</span> is said to be a surjection (onto function) iff <span class="math">\((\forall y \in \mathbb Y)(\exists x \in \mathbb X) f(x) = y\)</span></li>
<li>If <span class="math">\(f^{-1}\)</span> is a function from <span class="math">\(\mathbb Y \to \mathbb X\)</span> then <span class="math">\(f^{-1}\)</span> is called the inverse function for <span class="math">\(f\)</span>
<ul>
<li>Fact: <span class="math">\(f^{-1}\)</span> is a function iff <span class="math">\(f\)</span> is a <em>bijection</em> (1 to 1 and onto)</li>
</ul></li>
</ul></li>
<li><p>For some set <span class="math">\(\mathbb A\)</span> the image of <span class="math">\(\mathbb A\)</span> by <span class="math">\(f\)</span> is <span class="math">\(f(\mathbb A) = \{ f(x) : x \in \mathbb A \}\)</span>. We can also define the inverse of an image even when the function itself isn't invertible: <span class="math">\(f^{-1}(\mathbb A)\)</span></p></li>
</ul>
</div>

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<a href="https://abdulocra.cy/posts/eidma/">Introduction to Discrete Mathematics</a></h1>
<div class="post-meta">
<span class="post-date">
2019-11-04
2019-11-20
</span>
<span class="post-author">::
Abdulkadir</span>
</div>

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<generator>Hugo -- gohugo.io</generator>
<language>en-us</language>
<copyright>© Abdulkadir Furkan Şanlı 2019</copyright>
<lastBuildDate>Mon, 04 Nov 2019 00:00:00 +0000</lastBuildDate>
<lastBuildDate>Wed, 20 Nov 2019 00:00:00 +0000</lastBuildDate>
<atom:link href="https://abdulocra.cy/posts/index.xml" rel="self" type="application/rss+xml" />
@ -15,7 +15,7 @@
<item>
<title>Introduction to Discrete Mathematics</title>
<link>https://abdulocra.cy/posts/eidma/</link>
<pubDate>Mon, 04 Nov 2019 00:00:00 +0000</pubDate>
<pubDate>Wed, 20 Nov 2019 00:00:00 +0000</pubDate>
<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.