Commutativity: Difference between revisions
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imported>Richard Pinch (new article, just a stub) |
imported>Richard Pinch (def of commute) |
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:<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''. | ||
Revision as of 16:06, 5 November 2008
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.