# Commutative definition

*a*×

*b*=

*b*×

*a*, the operation indicated by × is commutative.

*a*+

*b*=

*b*+

*a*for any two numbers

*a*and

*b*, while subtraction is not commutative, since

*a*−

*b*¬eq;

*a*−

*b*unless both

*a*and

*b*are zero.

Independent of order. Used of a logical or mathematical operation that combines objects or sets of objects two at a time. If *a* × *b* = *b* × *a* , the operation indicated by × is commutative.

adjective

Relating to, involving, or characterized by substitution, interchange, or exchange.

adjective

Of commutation; involving exchange or replacement.

adjective

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

adjective

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(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.

adjective

(math.) Of or pertaining to an operation in which the order of the elements does not affect the result, as, in addition, 3 + 2 = 2 + 3 and, in multiplication, 2 × 3 = 3 × 2

adjective

Of or relating to binary operations for which changing the order of the inputs does not change the result of the operation. For example, addition is commutative, since *a* + *b* = * b* + *a* for any two numbers *a* and *b* , while subtraction is not commutative, since *a* − *b* ¬eq; *a* − *b* unless both *a* and *b* are zero.