# Commutative meaning

kŏm'yə-tā'tĭv, kə-myo͝o'tə-tĭv
Relating to, involving, or characterized by substitution, interchange, or exchange.
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.
Of commutation; involving exchange or replacement.
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
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 ab ¬eq; ab unless both a and b are zero.
(mathematics, 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 , it is true that .