From 00e119b90e349dd5b9debd77122a386bd81c5028 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Abdulkadir=20Furkan=20=C5=9Eanl=C4=B1?=
<abdulocracy@disroot.org>
Date: Wed, 27 Nov 2019 15:38:07 +0100
Subject: [PATCH] Regen
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
Signed-off-by: Abdulkadir Furkan Şanlı <abdulocracy@disroot.org>
---
public/posts/eidma/index.html | 21 +++++++++++++++++++++
1 file changed, 21 insertions(+)
diff --git a/public/posts/eidma/index.html b/public/posts/eidma/index.html
index d8bfb9f..c337591 100644
--- a/public/posts/eidma/index.html
+++ b/public/posts/eidma/index.html
@@ -363,6 +363,27 @@
</ul></li>
</ul></li>
<li>For some set <span class="math inline">\(\mathbb A\)</span> the image of <span class="math inline">\(\mathbb A\)</span> by <span class="math inline">\(f\)</span> is <span class="math inline">\(f(\mathbb A) = \{ f(x) : x \in \mathbb A \}\)</span>. We can also define the inverse of an image even when the function itself isn’t invertible: <span class="math inline">\(f^{-1}(\mathbb A)\)</span></li>
+</ul>
+<h2 id="combinatorics">Combinatorics</h2>
+<ul>
+<li><span class="math inline">\(|\mathbb A|\)</span> size (number of elements) of <span class="math inline">\(\mathbb A\)</span></li>
+<li>Rule of addition:
+<ul>
+<li>If <span class="math inline">\(\mathbb A, \mathbb B \subseteq \mathbb X\)</span> and <span class="math inline">\(|\mathbb A|, |\mathbb B| \in \mathbb N\)</span> and <span class="math inline">\(\mathbb A \cap \mathbb B = \emptyset\)</span> then <span class="math inline">\(|\mathbb A \cup \mathbb B| = |\mathbb A| + |\mathbb B|\)</span></li>
+<li>Can be generalized as: <span class="math display">\[
+(\forall n ) \mathbb{A}_1, \mathbb{A}_2, ..., \mathbb{A}_n \in \mathbb{X} \land \\
+|\mathbb{A}_1|, |\mathbb{A}_2|, ..., |\mathbb{A}_n| \in \mathbb{N} \implies \\
+(\forall i, j \in \{1, 2, ..., n \})(i \neq j \implies \mathbb{A}_i \cap \mathbb{A}_j = \emptyset)
+\]</span></li>
+</ul></li>
+<li>Rule of multiplication:
+<ul>
+<li><span class="math inline">\(\mathbb{A}, \mathbb{B} \subseteq \mathbb{X}, |\mathbb{A} \times \mathbb{B}| = |\mathbb{A}| \cdot |\mathbb{B}|\)</span></li>
+<li>Can be generalized as: <span class="math display">\[
+(\forall n ) \mathbb{A}_1, \mathbb{A}_2, ..., \mathbb{A}_n \in \mathbb{X} \land |\mathbb{A}_i| \in \mathbb{N} \implies \\
+|\mathbb{A}_1 \times \mathbb{A}_2 \times ... \times \mathbb{A}_n| = |\mathbb{A}_1| \cdot |\mathbb{A}_2| \cdot ... \cdot |\mathbb{A_n}|
+\]</span></li>
+</ul></li>
</ul>
</div>