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
Etymology
Origin of commutative
1525–35; < Medieval Latin commūtātīvus, equivalent to Latin commūtāt ( us ) (past participle of commūtāre; see commute, -ate 1) + -īvus -ive
Vocabulary lists containing commutative
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.
The commutative properties apply only to addition and multiplication!
From Textbooks • May 6, 2020
Since changing the order of the division did not give the same result, division is not commutative.
From Textbooks • Apr. 22, 2020
Unlike most operations we’ve seen, the cross product is not commutative.
From Textbooks • Mar. 30, 2016
Addition of vectors is commutative such that A + B = B + A .
From Textbooks • Aug. 12, 2015
For distributive justice directs distributions, while commutative justice directs commutations that can take place between two persons.
From Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province by Thomas, Aquinas, Saint
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.
