Idempotent vs Idempotently - What's the difference?
idempotent | idempotently |
(mathematics, computing) Describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed.
(mathematics) Said of an element of an algebraic structure (such as a group or semigroup) with a binary operation : that when the element operates on itself, the result is equal to itself.
(mathematics) Said of a binary operation : that all of the distinct elements it can operate on are idempotent (in the sense given just above).
(mathematics) Said of an algebraic structure : having an idempotent operation (in the sense above).
As an adjective idempotent
is describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed.As a noun idempotent
is an idempotent element.As an adverb idempotently is
in an idempotent way.idempotent
English
Adjective
(wikipedia idempotent) (-)- A projection operator is idempotent.
- Every finite semigroup has an idempotent element.
- Every group has a unique idempotent element: namely, its identity element.
- Since the AND logical operator is commutative, associative, and idempotent , then it distributes with respect to itself. (This is useful for understanding one of the conjunction rules of simplification to Prenex Normal Form, if the universal quantifier is thought of as a "big AND".)
Usage notes
Contrast with nullipotent, meaning has no'' side effects – doing it multiple times is the same as doing it ''zero'' times, rather than ''once, as in idempotent .Coordinate terms
* nilpotent * nullipotentReferences
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