# idempotent

### adjective

1. unchanged in value following multiplication by itself

*- this matrix is idempotent*

Similar word(s): unchanged

#### Sentences with idempotent as an adjective:

*- A projection operator is idempotent.Every finite semigroup has an idempotent element.*

*- Every group has a unique idempotent element: namely, its identity element.*

*- Since the AND logical operator is commutative, associative, and idempotent, then it distributes with respect to itself. (This is useful for understanding one of the conjunction rules of simplification to Prenex Normal Form, if the universal quantifier is thought of as a "big AND".)*

### noun

1. (mathematics) An idempotent element.

2. (mathematics) An idempotent structure.