# Definition:Idempotence/Relation

## Definition

Let $S$ be a set.

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

Then $\mathcal R$ is idempotent if and only if:

$\mathcal R \circ \mathcal R = \mathcal R$

where $\circ$ denotes composition of relations.