Idempotent

//ˌaɪ.dəmˈpoʊ.tənt// adj, noun

adj, noun ·Uncommon ·Advanced level

Definitions

Noun
  1. 1
    An idempotent element.
  2. 2
    An idempotent structure.
Adjective
  1. 1
    (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. not-comparable

    "A projection operator is idempotent."

  2. 2
    (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. not-comparable

    "Every finite semigroup has an idempotent element."

  3. 3
    (said of a binary operation) Such that all of the distinct elements it can operate on are idempotent (in the sense given just above). not-comparable

    "Since the AND logical operator is commutative, associative, and idempotent, it distributes with respect to itself."

  4. 4
    (said of an algebraic structure) Having an idempotent operation (in the sense given above). not-comparable
Adjective
  1. 1
    unchanged in value following multiplication by itself wordnet

Synonyms

All synonyms
nilpotentnullipotentunchanged

Example

More examples

"A projection operator is idempotent."

Etymology

From Latin roots idem (“same”) + potent (“having power”), thus “having the same power”. Coined in 1870 by American mathematician Benjamin Peirce in the context of algebra, later generalized to computer science.

Related phrases

algebraic structurebinary operation

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.