Definition:Equivalence Class/Representative

Definition

Let $S$ be a set.

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

Let $x \in S$.

Let $\eqclass x \RR$ be the equivalence class of $x$ under $\RR$.

Let $y \in \eqclass x \RR$.

Then $y$ is a representative of $\eqclass x \RR$.

Sources

• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $1$: Pairs, Relations, and Functions
• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.3$: Relations: Theorem $2.3.1$