commutative
Americanadjective
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of or relating to commutation, exchange, substitution, or interchange.
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Mathematics.
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(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.
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having reference to this property.
commutative law for multiplication.
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adjective
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relating to or involving substitution
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maths logic
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(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
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relating to this property
the commutative law of addition
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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.
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See also associative distributive
Other Word Forms
- commutatively adverb
- commutativity noun
- noncommutative adjective
- uncommutative adjective
- uncommutatively adverb
- uncommutativeness noun
Etymology
Origin of commutative
1525–35; < Medieval Latin commūtātīvus, equivalent to Latin commūtāt ( us ) (past participle of commūtāre; commute, -ate 1 ) + -īvus -ive
Example Sentences
Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.
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
Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023
Idioms from The American Heritage® Idioms Dictionary copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.
