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

/ kə-myo̅o̅′tə-tĭv,kŏm′yə-tā′tĭv /

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

Derived Forms

• comˈmutatively, adverb

Other Words From

• com·muta·tive·ly adverb
• com·muta·tivi·ty noun
• non·commu·tative adjective
• uncom·muta·tive adjective
• uncom·muta·tive·ly adverb
• uncom·muta·tive·ness 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.

From Scientific American

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

From MSNBC

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.

From Nature

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

From Scientific American

"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.

From New York Times

Related Words

• capricious
• fickle
• fluctuating
• mercurial
• protean
• shifting
• unpredictable
• unsettled
• unstable
• varying
• volatile