\begin{definition}[Definition:Idempotence/Element]
Let $S$ be a set.
Let $\circ: S \times S \to S$ be a binary operation on $S$.
Let $x \in S$ have the property that $x \circ x = x$.
Then $x \in S$ is described as '''idempotent under the operation $\circ$'''.
\end{definition}