\begin{definition}[Definition:Idempotence/Operation]
Let $S$ be a set.
Let $\circ: S \times S \to S$ be a binary operation on $S$.
If ''all'' the elements of $S$ are idempotent under $\circ$, then the term can be applied to the operation itself:
The binary operation $\circ$ is '''idempotent''' {{iff}}:
:$\forall x \in S: x \circ x = x$
\end{definition}