Definition:Idempotence/Mapping

Definition
Let $f: S \to S$ be a mapping.

Then $f$ is idempotent iff:
 * $\forall x \in S: f \left({f \left({x}\right)}\right) = f \left({x}\right)$

That is, iff applying the same mapping a second time to an argument gives the same result as applying it once.

And of course, that means the same as applying it as many times as you want.