\begin{definition}[Definition:Quotient Set]
Let $\RR$ be an equivalence relation on a set $S$.
For any $x \in S$, let $\eqclass x \RR$ be the $\RR$-equivalence class of $x$.
The '''quotient set of $S$ induced by $\RR$''' is the set $S / \RR$ of $\RR$-classes of $\RR$:
:$S / \RR := \set {\eqclass x \RR: x \in S}$
\end{definition}