# commutative

## commutative

[kuh-myoo-tuh-tiv, kom-yuh-tey-tiv]
adjective
1.
of or pertaining to commutation, exchange, substitution, or interchange.
2.
Mathematics.
a.
(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.
b.
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

commutatively, adverb
commutativity, noun
noncommutative, adjective
uncommutative, adjective
uncommutatively, adverb
uncommutativeness, noun
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
 commutative (kəˈmjuːtətɪv, ˈkɒmjʊˌteɪtɪv) —adj 1. relating to or involving substitution 2. maths, logic a.  (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 b.  relating to this property: the commutative law of addition com'mutatively —adv

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Etymonline
Word Origin & History

commutative
1530s, from M.L. commutativus, from L. commutat-, pp. stem of commutare (see commute).
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Science Dictionary
 commutative  [%PREMIUM_LINK%]     (kə-my'tə-tĭv, kŏm'yə-tā'tĭv)  Pronunciation Key  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.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Example sentences
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.
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