Commutativity: Difference between revisions
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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> | ||
for all ''x'' and ''y''. | 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 [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context commutativity is often referred to as the ''commutative law''. | Examples of commutative operations are [[addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context commutativity is often referred to as the ''commutative law''. | ||
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==See also== | ==See also== | ||
* [[Commutator]] | * [[Commutator]] | ||
* [[Commutative diagram]][[Category:Suggestion Bot Tag]] | |||
Latest revision as of 11:00, 31 July 2024
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.