Difference between revisions of "Commutative property"
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In mathematics, the '''commutative property''' states that a [[binary operation]] <math>*</math> on a set '''A''' is said to be commutative if for all <math>x,y</math> in '''A''' we have <math>x*y=y*x</math>. An Example of a commutative operation is [[addition]] in the [[real numbers]]. When a [[Group (mathematics)|group]]'s operation is commutative, it is said to be [[abelian]]. | In mathematics, the '''commutative property''' states that a [[binary operation]] <math>*</math> on a set '''A''' is said to be commutative if for all <math>x,y</math> in '''A''' we have <math>x*y=y*x</math>. An Example of a commutative operation is [[addition]] in the [[real numbers]]. When a [[Group (mathematics)|group]]'s operation is commutative, it is said to be [[abelian]]. | ||
| − | In layman | + | In layman terms, an equation demonstrates commutativity when the constants or variables can be moved around an operation without changing the answer (e.g. 1 + 2 = 2 + 1 or 2 * 3 = 3 * 2). |
It is as if the numbers are "commuting" from one place to another. | It is as if the numbers are "commuting" from one place to another. | ||
Revision as of 21:26, November 23, 2008
In mathematics, the commutative property states that a binary operation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle *} on a set A is said to be commutative if for all in A we have . An Example of a commutative operation is addition in the real numbers. When a group's operation is commutative, it is said to be abelian.
In layman terms, an equation demonstrates commutativity when the constants or variables can be moved around an operation without changing the answer (e.g. 1 + 2 = 2 + 1 or 2 * 3 = 3 * 2). It is as if the numbers are "commuting" from one place to another.
The commutative property implies the associative property.