idempotent
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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.
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
French
Pronunciation
Audio (file)
Adjective
idempotent (feminine idempotente, masculine plural idempotents, feminine plural idempotentes)
German
Pronunciation
Audio (file)
Adjective
idempotent (strong nominative masculine singular idempotenter, not comparable)
Declension
Positive forms of idempotent (uncomparable)
Swedish
Adjective
idempotent
Turkish
Adjective
idempotent