View synonyms for commutative

commutative

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

Phonetic (Standard)IPA

adjective

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

/ kəˈmjuːtətɪv; ˈkɒmjʊˌteɪtɪv /

relating to or involving substitution
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 /

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

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

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

Among equals, it is called commutative justice, the which alone is here in question.

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

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

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

April 18, 2024petrichor

[pet-ri-kawr]

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