# Definition:Equivalence Class/Representative

## Definition

Let $S$ be a set.

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

Let $x \in S$.

Let $\eqclass x {\mathcal R}$ be the equivalence class of $x$ under $\mathcal R$.

Let $y \in \eqclass x {\mathcal R}$.

Then $y$ is a representative of $\eqclass x {\mathcal R}$.