commutative

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adjective

Such that the order in which the operands are taken does not affect their image under the operation.

“Addition and multiplication are commutative operations but subtraction and division are not.”

Similar
abelianindependent
Opposite
anticommutative
OriginFrench commuter →
Less commonScrabble 20
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Meanings

adjectivecommutative (not comparable)
  1. not comparablemathematicsSuch that the order in which the operands are taken does not affect their image under the operation.

    Addition and multiplication are commutative operations but subtraction and division are not.

    2 more examples

    Addition on the real numbers is commutative because for any real numbers s,t, it is true that s#43;t#61;t#43;s.

    The associativity of OR and AND is not at all obvious. It is tempting to assume that because OR and AND are commutative that they must be associative also. This is not the case, however, and some commutative Boolean operators are not associative. Examples include NAND and NOR.

    2022 August 4, William Bahn, “Boolean Algebra Laws—Delving Into Boolean Identities”, in All About Circuits
  2. not comparablealgebraHaving a commutative operation.

    Synonyms: abelian, Abelian

  3. not comparablemathematicsSuch that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
  4. not comparableRelating to exchange; interchangeable.

Synonyms & antonyms

adjectiveHaving a commutative operation.

Similar
abelianAbelian
Opposite
anticommutative

More synonyms by meaning

adjective(of a binary operation) independent of order; as in e.g.: ‘a x b’ = ‘b x a’

Similar
independent

Synonym sets from Open English WordNet, CC BY 4.0.

Origin

  1. Frenchcommuter“to substitute or switch”
  2. Englishcommutative

From French commuter (“to substitute or switch”) + -ative (“tending to”). See commute.

More words from French

Full word history & related roots →

Translations

Catalan commutatiu, commutatiu
  • commutatiumathematics: such that order of operands does not affect result
  • commutatiualgebra: having a commutative operation
Chinese Mandarin 可交換的 /可交换的, 可交換的 /可交换的
  • 可交換的 /可交换的mathematics: such that order of operands does not affect result
  • 可交換的 /可交换的algebra: having a commutative operation
Czech komutativní, komutativní
  • komutativnímathematics: such that order of operands does not affect result
  • komutativníalgebra: having a commutative operation
Danish kommutativ
  • kommutativmathematics: such that order of operands does not affect result
Dutch commutatief
  • commutatiefmathematics: such that order of operands does not affect result
Esperanto komuta, komuta
  • komutamathematics: such that order of operands does not affect result
  • komutaalgebra: having a commutative operation
Finnish kommutatiivinen, vaihdannainen
  • kommutatiivinenmathematics: such that order of operands does not affect result
  • vaihdannainenmathematics: such that order of operands does not affect result
  • kommutatiivinenalgebra: having a commutative operation
  • vaihdannainenalgebra: having a commutative operation
French commutatif
  • commutatifmathematics: such that order of operands does not affect result
German kommutativ, kommutativ
  • kommutativmathematics: such that order of operands does not affect result
  • kommutativalgebra: having a commutative operation
Greek αντιμεταθετικός
  • αντιμεταθετικός (antimetathetikós)mathematics: such that order of operands does not affect result
Hindi विनिमेय
  • विनिमेय (vinimey)mathematics: such that order of operands does not affect result
Icelandic víxlinn
  • víxlinnmathematics: such that order of operands does not affect result
Indonesian komutatif, komutatif
  • komutatifmathematics: such that order of operands does not affect result
  • komutatifalgebra: having a commutative operation
Italian commutativo
  • commutativomathematics: such that order of operands does not affect result
Polish przemienny, przemienny
  • przemiennymathematics: such that order of operands does not affect result
  • przemiennyalgebra: having a commutative operation
Portuguese comutativo, comutativo
  • comutativomathematics: such that order of operands does not affect result
  • comutativoalgebra: having a commutative operation
Romanian comutativ, comutativ
  • comutativmathematics: such that order of operands does not affect result
  • comutativalgebra: having a commutative operation
Russian коммутативный, перестановочный
  • коммутативный (kommutativnyj)mathematics: such that order of operands does not affect result
  • перестановочный (perestanovočnyj)mathematics: such that order of operands does not affect result
Tagalog palitin, palitin
  • palitinmathematics: such that order of operands does not affect result
  • palitinalgebra: having a commutative operation
Turkish değişmeli, değişmeli
  • değişmelimathematics: such that order of operands does not affect result
  • değişmelialgebra: having a commutative operation
Cite this entry
APA

commutative. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/commutative

MLA

“commutative.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/commutative. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “commutative,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/commutative.

Source: commutative on Wiktionary, CC BY-SA 4.0.