Idempotence

In mathematics idempotence is the property of an operation that repeated application has no effect.

A binary operation $$\star$$ is idempotent if


 * $$x \star x = x$$ for all x:

equivalently, every element is an idempotent element for $$\star$$.

Examples of idempotent binary operations include join and meet in a lattice.

A unary operation (function from a set to itself) π is idempotent if it is an idempotent element for function composition, π2 = π.