Commutativity: Difference between revisions
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imported>Richard Pinch (def of commute) |
imported>Howard C. Berkowitz No edit summary |
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In [[algebra]], '''commutativity''' is a property of [[binary operation]]s or of [[operator]]s on a set. If <math>\star</math> is a binary operation then the commutative property is the condition that | {{subpages}} | ||
In [[algebra]], '''commutativity''' is a property of [[binary operation]]s or of [[operator (mathematics)|operator]]s on a set. If <math>\star</math> is a binary operation then the commutative property is the condition that | |||
:<math> x \star y = y \star x \,</math> | :<math> x \star y = y \star x \,</math> | ||
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==See also== | ==See also== | ||
* [[Commutator]] | * [[Commutator]] | ||
* [[Commutative diagram]] | |||
Latest revision as of 19:40, 31 January 2009
In algebra, commutativity is a property of binary operations or of operators on a set. If is a binary operation then the commutative property is the condition that
for all x and y. If this equality holds for a particular pair of elements, they are said to commute.
Examples of commutative operations are addition and multiplication of integers, rational numbers, real and complex numbers. In this context commutativity is often referred to as the commutative law.