Idempotence

Summary

Idempotence is the property of something that gives the same result when it is applied twice as when it is applied once. An element $x$ is idempotent for a binary operation $\ast$ when $x \ast x = x$, and a function $f$ is idempotent when $f \circ f = f$. Lattice operations, projections and closure operators are idempotent. The idempotent elements of a ring are the idempotents for its multiplication.