Definition:Idempotence/Element

Definition
Let $\circ: S \times S \to S$ be a binary operation.

The element $x \in S$ is idempotent under the operation $\circ$ iff $x \circ x = x$.

For example, $0$ is idempotent under the operation of addition in the set of integers $\Z$, but no other element of $\Z$ is so.