different between idempotent vs idempotently
idempotent
English
Etymology
Latin roots, idem (“same”) +? potent (“having power”) – literally, “having the same power”.
Coined 1870 by American mathematician Benjamin Peirce in context of algebra.
Pronunciation
- (US) IPA(key): /a?.d?m?po?.t?nt/, /?.d?m?po?.t?nt/
Adjective
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.
- (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.
- (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, then it distributes with respect to itself.
- (mathematics) Said of an algebraic structure: having an idempotent operation (in the sense above).
Usage notes
See the Usage notes section of nullipotent.
Coordinate terms
- nilpotent
- nullipotent
Related terms
- idempotence
- nilpotent
- nullipotent
- unipotent
Translations
Noun
idempotent (plural idempotents)
- (mathematics) An idempotent element.
- (mathematics) An idempotent structure.
References
- “idempotent” at FOLDOC
German
Pronunciation
Adjective
idempotent
- idempotent
Swedish
Adjective
idempotent
- idempotent
Turkish
Adjective
idempotent
- idempotent
idempotent From the web:
idempotently
English
Etymology
idempotent +? -ly
Adverb
idempotently (not comparable)
- In an idempotent way.
idempotently From the web:
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