idempotent
English
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
- (US) IPA(key): /aɪ.dəmˈpoʊ.tənt/, /ɪ.dəmˈpoʊ.tənt/, /aɪˈdɛm.pə.tənt/
Audio (US) (file)
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.
French
Pronunciation
Audio (file)
Adjective
idempotent (feminine idempotente, masculine plural idempotents, feminine plural idempotentes)
German
Pronunciation
Audio (file)
Declension
Positive forms of idempotent (uncomparable)
| number & gender | singular | plural | |||
|---|---|---|---|---|---|
| masculine | feminine | neuter | |||
| predicative | er ist idempotent | sie ist idempotent | es ist idempotent | sie sind idempotent | |
| strong declension (without article) |
nominative | idempotenter | idempotente | idempotentes | idempotente |
| genitive | idempotenten | idempotenter | idempotenten | idempotenter | |
| dative | idempotentem | idempotenter | idempotentem | idempotenten | |
| accusative | idempotenten | idempotente | idempotentes | idempotente | |
| weak declension (with definite article) |
nominative | der idempotente | die idempotente | das idempotente | die idempotenten |
| genitive | des idempotenten | der idempotenten | des idempotenten | der idempotenten | |
| dative | dem idempotenten | der idempotenten | dem idempotenten | den idempotenten | |
| accusative | den idempotenten | die idempotente | das idempotente | die idempotenten | |
| mixed declension (with indefinite article) |
nominative | ein idempotenter | eine idempotente | ein idempotentes | (keine) idempotenten |
| genitive | eines idempotenten | einer idempotenten | eines idempotenten | (keiner) idempotenten | |
| dative | einem idempotenten | einer idempotenten | einem idempotenten | (keinen) idempotenten | |
| accusative | einen idempotenten | eine idempotente | ein idempotentes | (keine) idempotenten | |
Swedish
Turkish
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