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 $\left[\!\left[{x}\right]\!\right]_\mathcal R$ be the equivalence class of $x$ under $\mathcal R$.

Let $y \in \left[\!\left[{x}\right]\!\right]_\mathcal R$.

Then $y$ is a '''representative of $\left[\!\left[{x}\right]\!\right]_\mathcal R$.