Definition:Idempotence/Operation

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

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:
 * $\forall x \in S: x \circ x = x$

Also see
Examples of idempotent operations:
 * Union is Idempotent Operation: $\cup$
 * Intersection is Idempotent Operation: $\cap$