\begin{definition}[Definition:Idempotence/Relation]
Let $S$ be a set.
Let $\RR \subseteq S \times S$ be a relation on $S$.
Then $\RR$ is '''idempotent''' {{iff}}:
:$\RR \circ \RR = \RR$
where $\circ$ denotes composition of relations.
\end{definition}