afk/personal-site
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Edit eidma.mmark and regen

Browse Source
This commit is contained in:
Abdulkadir Furkan Şanlı
2019-11-04 16:53:52 +01:00
parent 015ab76c04
commit 954dfc1f36
2 changed files with 6 additions and 6 deletions
Download Patch File Download Diff File Expand all files Collapse all files

8
content/posts/eidma.mmark
View File

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