commutative en · ADJ
Pronunciation
- (US) audio
Etymology
From French commuter (“to substitute or switch”) + -ative (“tending to”). See commute.
Meanings
-
(not-comparable, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.
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:Addition and multiplication are commutative operations but subtraction and division are not.
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.
- (not-comparable, of an algebraic structure) Having a commutative operation.
- (not-comparable, of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
- (not-comparable) Relating to exchange; interchangeable.
Antonyms
Deriveds
cocommutative · commutatively · gyrocommutative · supercommutative · commutativeness · commutative property · commutativity · commutative group · uncommutative · noncommutative · commutative algebra · combinatorial commutative algebra · commutative ring · commutative justice
Relateds
Synonyms
Abelian (of an algebraic structure) · abelian (of an algebraic structure)
Translations (35)
fi vaihdannainen (algebra: having a commutative operation) · cs komutativní (algebra: having a commutative operation) · el αντιμεταθετικός (mathematics: such that order of operands does not affect result) · pl przemienny (algebra: having a commutative operation) · ro comutativ (algebra: having a commutative operation) · pt comutativo (algebra: having a commutative operation) · ca commutatiu (algebra: having a commutative operation) · fi kommutatiivinen (algebra: having a commutative operation) · de kommutativ (algebra: having a commutative operation) · hi विनिमेय (mathematics: such that order of operands does not affect result) · ru перестановочный (mathematics: such that order of operands does not affect result) · ca commutatiu (mathematics: such that order of operands does not affect result) · fr commutatif (mathematics: such that order of operands does not affect result) · cmn 可交換的 /可交换的 (algebra: having a commutative operation) · da kommutativ (mathematics: such that order of operands does not affect result) · cmn 可交換的 /可交换的 (mathematics: such that order of operands does not affect result) · it commutativo (mathematics: such that order of operands does not affect result) · id komutatif (mathematics: such that order of operands does not affect result) · pt comutativo (mathematics: such that order of operands does not affect result) · tr değişmeli (mathematics: such that order of operands does not affect result) · fi kommutatiivinen (mathematics: such that order of operands does not affect result) · tr değişmeli (algebra: having a commutative operation) · pl przemienny (mathematics: such that order of operands does not affect result) · de kommutativ (mathematics: such that order of operands does not affect result) · cs komutativní (mathematics: such that order of operands does not affect result) · nl commutatief (mathematics: such that order of operands does not affect result) · ru коммутативный (mathematics: such that order of operands does not affect result) · ro comutativ (mathematics: such that order of operands does not affect result) · tl palitin (mathematics: such that order of operands does not affect result) · eo komuta (mathematics: such that order of operands does not affect result) · id komutatif (algebra: having a commutative operation) · tl palitin (algebra: having a commutative operation) · fi vaihdannainen (mathematics: such that order of operands does not affect result) · is víxlinn (mathematics: such that order of operands does not affect result) · eo komuta (algebra: having a commutative operation)