COMMUTATIVE

commutative

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

Source: WordNet® 3.1


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 \(s,t\), it is true that \(s+t=t+s\).

(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


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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Word of the Day

29 November 2024

POPULATED

(adjective) furnished with inhabitants; “the area is well populated”; “forests populated with all kinds of wild life”


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Coffee Trivia

The word “coffee” entered the English language in 1582 via the Dutch “koffie,” borrowed from the Ottoman Turkish “kahve,” borrowed in turn from the Arabic “qahwah.” The Arabic word qahwah was traditionally held to refer to a type of wine.

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