idempotent

Pronunciation

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Pronunciation

- (
*America*) IPA: /aɪ.dəmˈpoʊ.tənt/, /ɪ.dəmˈpoʊ.tənt/

**idempotent** (*not comparable*)

- (
*mathematics, computing*)*Said of a function*: describing an action which, when performed multiple times on the same subject, has no further effect on its subject after the first time it is performed.- A projection operator is
**idempotent**.

- A projection operator is
- (
*mathematics*)*Said of an element of an algebraic structure with a binary operation (such as a group or semigroup)*: when the element operates on itself, the result is equal to itself.- Every finite semigroup has an
**idempotent**element. - Every group has a unique
**idempotent**element: namely, its identity element.

- Every finite semigroup has an
- (
*mathematics*)*Said of a binary operation*: that all of the distinct elements it can operate on are idempotent (in the sense given just above).- Since the AND logical operator is commutative, associative, and
**idempotent**, then it distributes with respect to itself.

- Since the AND logical operator is commutative, associative, and
- (
*mathematics*)*Said of an algebraic structure*: having an idempotent operation (in the sense above).

- German: idempotent
- Russian: идемпоте́нтный

- Spanish: idempotente

**idempotent** (*plural* idempotents)

- (
*mathematics*) An idempotent element. - (
*mathematics*) An idempotent structure.

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