Category:Equivalence Classes

From ProofWiki
Jump to navigation Jump to search

This category contains results about Equivalence Classes.
Definitions specific to this category can be found in Definitions/Equivalence Classes.

Let $S$ be a set.

Let $\RR \subseteq S \times S$ be an equivalence relation on $S$.

Let $x \in S$.

Then the equivalence class of $x$ under $\RR$ is the set:

$\eqclass x \RR = \set {y \in S: \tuple {x, y} \in \RR}$