commutative
adjEtymology From French commuter (“to substitute or switch”) + -ative (“tending to”). See commute.
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Mathematics, Sciences 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#43;t#61;t#43;s.
- Addition and multiplication are commutative operations but subtraction and division are not.
1 more example
- 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:
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Algebra, Mathematics, Sciences Of an algebraic structure Having a commutative operation.
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Mathematics, Sciences Of a diagram of morphisms Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
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Relating to exchange; interchangeable.
- Synonyms
- abelian, Abelian
- Antonyms
- anticommutative
- Derived terms
- cocommutative, combinatorial commutative algebra, commutative algebra, commutative group, commutative justice, commutatively, commutativeness, commutative property, commutative ring, commutativity, gyrocommutative, noncommutative, supercommutative, uncommutative
- Related terms
- commutator, commute