# commutative

[ kuh-myoo-tuh-tiv, kom-yuh-tey-tiv ]

/ kəˈmyu tə tɪv, ˈkɒm yəˌteɪ tɪv /

### adjective

of or relating to commutation, exchange, substitution, or interchange.

Mathematics.

- (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.
- having reference to this property: commutative law for multiplication.

## RELATED WORDS

protean, unsettled, varying, capricious, unpredictable, fickle, unstable, volatile, mercurial, fluctuating, mutable, changeful, agitated, convertible, fitful, flighty, fluid, impulsive, inconstant, indecisive

## Nearby words

- communize,
- commutable,
- commutate,
- commutation,
- commutation ticket,
- commutative group,
- commutative law,
- commutator,
- commutator group,
- commute

## Origin of commutative

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

## Examples from the Web for commutative

Negative Numbers may be regarded as resulting from the commutative law for addition and subtraction.

This is included in the preceding, but it is simpler in that the various operations are commutative.

Often the meaning of a sentence tacitly implies that the commutative law does not hold.

“Simple” practice involves an application of the commutative law.

## commutative

/ (kəˈmjuːtətɪv, ˈkɒmjʊˌteɪtɪv) /

### adjective

relating to or involving substitution

maths logic

- (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
- relating to this propertythe commutative law of addition

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## commutative

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

Online Etymology Dictionary, © 2010 Douglas Harper

## commutative

[ kə-myōō′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.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.