# Commutative meaning

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

adjective

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

Of commutation; involving exchange or replacement.

adjective

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

adjective

(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