Category:Definitions/Equivalence Classes

This category contains definitions related to Equivalence Classes.
Related results can be found in Category: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:

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