COMMUTATIVE

commutative

(adjective) (of a binary operation) independent of order; as in e.g. “a x b = b x a”

Source: WordNet® 3.1

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Etymology

Adjective

commutative (not comparable)

(mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.

Addition on the real numbers is commutative because for any real numbers $\backslash (s,t\backslash )$, it is true that $\backslash (s+t=t+s\backslash )$.

(algebra, of an algebraic structure) Having a commutative operation.

(mathematics, of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.

Relating to exchange; interchangeable.

Synonyms

• (of an algebraic structure): abelian, Abelian

Antonyms

• anticommutative

Source: Wiktionary

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Com*mut"a*tive, a. Etym: [CF. F. commutatif.]

Definition: Relative to exchange; interchangeable; reciprocal.

– Com*mut"a*tive"ly, adv. Rich traders, from their success, are presumed . . . to have cultivated an habitual regard to commutative justice. Burke.

Source: Webster’s Unabridged Dictionary 1913 Edition

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