commutative

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

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.

commutative

/ ˈkɒmjʊˌteɪtɪv, kəˈmjuːtətɪv /

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

commutative

1. 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.

2. See also associative distributive

Other Word Forms

• commutatively adverb
• commutativity noun
• noncommutative adjective
• uncommutative adjective
• uncommutatively adverb
• uncommutativeness noun

Word History and Origins

Origin of commutative¹

1525–35; < Medieval Latin commūtātīvus, equivalent to Latin commūtāt ( us ) (past participle of commūtāre; commute, -ate ¹ ) + -īvus -ive

Example Sentences

Noether’s theory of ideals and commutative rings forms a foundation for any researcher in the field of higher algebra.

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And then there is commutative justice, the kind that governs the one-on-one relationships we have with each other.

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He proposed that a geometric object called a scheme was associated to any commutative ring — that is, a set in which addition and multiplication are defined and multiplication is commutative, a × b = b × a.

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As a quantum physicist he would have been acutely aware that at the deepest level, nature disobeys the commutative law.

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"Math, I always thought was easy," he told the class, which had been listening to a lecture about the commutative property before the mayor's entourage descended on the classroom.

Read more on New York Times

Related Words

• capricious 
• fickle 
• fluctuating www.thesaurus.com
• mercurial 
• protean 
• shifting www.thesaurus.com
• unpredictable 
• unsettled 
• unstable 
• varying www.thesaurus.com
• volatile