commutative

[kuh-myoo-tuh-tiv, kom-yuh-tey-tiv] /kəˈmyu tə tɪv, ˈkɒm yəˌteɪ tɪv/
adjective
1.
of or relating to commutation, exchange, substitution, or interchange.
2.
Mathematics.
  1. (of a binary operation) having the property that one term operating on a second is equal to the second operating on the first, as a × b = b × a.
  2. having reference to this property:
    commutative law for multiplication.
Origin
1525-35; < Medieval Latin commūtātīvus, equivalent to Latin commūtāt(us) (past participle of commūtāre; see commute, -ate1) + -īvus -ive
Related forms
commutatively, adverb
commutativity, noun
noncommutative, adjective
uncommutative, adjective
uncommutatively, adverb
uncommutativeness, noun
Examples from the web for commutative
  • In arithmetic, operations are interchangeable if they are commutative.
  • All anybody needs to know about mathematics is that the commutative property of addition exists only in the human imagination.
  • Students are able to recognize and use the commutative property of addition and multiplication.
  • Identifies symbolic representations of the commutative property.
  • Addition and multiplication are commutative, while subtraction is not.
  • Products are sorted into a canonical order using the commutative law.
British Dictionary definitions for commutative

commutative

/kəˈmjuːtətɪv; ˈkɒmjʊˌteɪtɪv/
adjective
1.
relating to or involving substitution
2.
(maths, logic)
  1. (of an operator) giving the same result irrespective of the order of the arguments; thus disjunction and addition are commutative but implication and subtraction are not
  2. relating to this property: the commutative law of addition
Derived Forms
commutatively, adverb
Word Origin and History for commutative
adj.

1530s, from Medieval Latin commutativus, from Latin commutat-, past participle stem of commutare (see commute (v.)).

commutative in Science
commutative
(kə-my'tə-tĭv, kŏm'yə-tā'tĭv)
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 ` a - b unless both a and b are zero. See also associative, distributive.