# Idempotence

A property of a binary operation. For the logical operation of conjunction ($\wedge$) and disjunction ($\vee$) is expressed by the following identities: $$a \wedge a = a\ \ \text{and}\ \ a \vee a = a \ .$$
A general binary operation $\star$ is idempotent if the identity $$a \star a = a$$ is valid in the given algebraic system: that is, every element $a$ of the given system is an idempotent.