idempotent
From Wiktionary, the free dictionary
Etymology
Latin roots, idem (“same”) + potent (“having power”) – literally, “having the same power”. Coined in 1870 by American mathematician Benjamin Peirce in the context of algebra.[1]
Pronunciation
Adjective
idempotent (not comparable)
- (mathematics, computing) (said of a function) Such that, when performed multiple times on the same subject, it has no further effect on its subject after the first time it is performed.
- A projection operator is idempotent.
- (mathematics) (said of an element of an algebraic structure with a binary operation, such as a group or semigroup) Such that, when it 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.
- (mathematics) (said of a binary operation) Such 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, it distributes with respect to itself.
- (mathematics) (said of an algebraic structure) Having an idempotent operation (in the sense given above).
Usage notes
- See the Usage notes section of nullipotent.
Coordinate terms
Related terms
Translations
mathematics: an action which, when performed multiple time, has no further effect on its subject after the first time it is performed
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mathematics: Said of an element of an algebraic structure with a binary operation: that when the element operates on itself, the result is equal to itself
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Said of a binary operation: that all of the distinct elements it can operate on are idempotent
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See also
Noun
idempotent (plural idempotents)
- (mathematics) An idempotent element.
- (mathematics) An idempotent structure.
References
- Polcino & Sehgal (2002), p. 127
- “idempotent” at FOLDOC
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