Commutative

Quick meaning: Commutative is an adjective meaning (mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.

Meaning

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

More Meanings

1. (algebra, of an algebraic structure) Having a commutative operation.
2. Relating to exchange; interchangeable.
3. (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.

Example Sentences

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.

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.

Synonyms for commutative

Depending on context, synonyms include abelian, independent.

Antonyms for commutative

Common opposites include anticommutative.

Related Words

Related dictionary entries include independent, monoid, semigroup, semigroups, abelian, anticommuting.

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