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Edit eidma.mmark and regen

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Abdulkadir Furkan Şanlı 2019-11-04 16:53:52 +01:00
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content/posts/eidma.mmark
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@ -115,10 +115,10 @@ markup = "mmark"
- Def: A relation $$R$$ on a set $$\mathbb X$$ is a subset of $$\mathbb X \times \mathbb X$$ ($$R \subseteq \mathbb X \times \mathbb X$$) - Def: A relation $$R$$ on a set $$\mathbb X$$ is a subset of $$\mathbb X \times \mathbb X$$ ($$R \subseteq \mathbb X \times \mathbb X$$)
- Graph of a function $$f()$$: $$\{ (x, f(x) : x \in Dom(f) \}$$ - Graph of a function $$f()$$: $$\{ (x, f(x) : x \in Dom(f) \}$$
- Properties of: - Properties of:
1. Reflexivity: $$(\forall x \in \mathbb X ) (x, x) \in R \equiv (\forall x \in \mathbb X) x R x$$ - Reflexivity: $$(\forall x \in \mathbb X ) (x, x) \in R \equiv (\forall x \in \mathbb X) x R x$$
2. Symmetricity: $$[ (\forall x, y \in \mathbb X) (x, y) \in R \implies (y, x) \in R) ] \equiv [ (\forall x, y \in \mathbb X) ( x R y \implies y R x) ]$$ - Symmetricity: $$[ (\forall x, y \in \mathbb X) (x, y) \in R \implies (y, x) \in R) ] \equiv [ (\forall x, y \in \mathbb X) ( x R y \implies y R x) ]$$
3. Transitivity: $$(\forall x, y, z \in \mathbb X) (x R y \land y R z \implies x R z)$$ - Transitivity: $$(\forall x, y, z \in \mathbb X) (x R y \land y R z \implies x R z)$$
4. Antisymmetricity: $$(\forall x, y \in \mathbb X) (x R y \land y R x \implies x = y)$$ - Antisymmetricity: $$(\forall x, y \in \mathbb X) (x R y \land y R x \implies x = y)$$
- Equivalence relations: - Equivalence relations:
- Def: $$R \subseteq \mathbb X \times \mathbb X$$ is said to be an equivalence relation *iff* $$R$$ is reflexive, symmetric and transitive. - Def: $$R \subseteq \mathbb X \times \mathbb X$$ is said to be an equivalence relation *iff* $$R$$ is reflexive, symmetric and transitive.

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public/posts/eidma/index.html
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@ -345,12 +345,12 @@
<li><p>Properties of:</p> <li><p>Properties of:</p>
<ol> <ul>
<li>Reflexivity: <span class="math">\((\forall x \in \mathbb X ) (x, x) \in R \equiv (\forall x \in \mathbb X) x R x\)</span></li> <li>Reflexivity: <span class="math">\((\forall x \in \mathbb X ) (x, x) \in R \equiv (\forall x \in \mathbb X) x R x\)</span></li>
<li>Symmetricity: <span class="math">\([ (\forall x, y \in \mathbb X) (x, y) \in R \implies (y, x) \in R) ] \equiv [ (\forall x, y \in \mathbb X) ( x R y \implies y R x) ]\)</span></li> <li>Symmetricity: <span class="math">\([ (\forall x, y \in \mathbb X) (x, y) \in R \implies (y, x) \in R) ] \equiv [ (\forall x, y \in \mathbb X) ( x R y \implies y R x) ]\)</span></li>
<li>Transitivity: <span class="math">\((\forall x, y, z \in \mathbb X) (x R y \land y R z \implies x R z)\)</span></li> <li>Transitivity: <span class="math">\((\forall x, y, z \in \mathbb X) (x R y \land y R z \implies x R z)\)</span></li>
<li>Antisymmetricity: <span class="math">\((\forall x, y \in \mathbb X) (x R y \land y R x \implies x = y)\)</span></li> <li>Antisymmetricity: <span class="math">\((\forall x, y \in \mathbb X) (x R y \land y R x \implies x = y)\)</span></li>
</ol></li> </ul></li>
<li><p>Equivalence relations:</p> <li><p>Equivalence relations:</p>