Definition:Idempotence/Operation

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

Also see

 * Set Union is Idempotent
 * Set Intersection is Idempotent