Idempotence

In mathematics idempotence is the property of an operation that repeated application has no further 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; union and intersection on sets; disjunction and conjunction in propositional logic.

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