Last modified on 23 May 2014, at 13:43

idempotent

EnglishEdit

EtymologyEdit

Latin roots, idem (same) +‎ potent (having power) – literally, “having the same power”.

Coined 1870 by American mathematician Benjamin Peirce in context of algebra.[1]

AdjectiveEdit

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Wikipedia

idempotent (not comparable)

  1. (mathematics, computing) Describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed.
    A projection operator is idempotent.
    Every finite semigroup has an idempotent element.
  2. (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.
    Every group has a unique idempotent element: namely, its identity element.
  3. (mathematics) Said of a binary operation: 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. (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 notesEdit

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.

Related termsEdit

Coordinate termsEdit

TranslationsEdit

NounEdit

idempotent (plural idempotents)

  1. An idempotent ring or other structure

ReferencesEdit

  1. ^ Polcino & Sehgal (2002), p. 127

GermanEdit

AdjectiveEdit

idempotent

  1. idempotent

SwedishEdit

AdjectiveEdit

idempotent

  1. idempotent

TurkishEdit

AdjectiveEdit

idempotent

  1. idempotent