# 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 | + | 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 set of [[real numbers]]. When a [[Group (mathematics)|group]]'s operation is commutative, it is said to be [[abelian]]. |

− | In layman's 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). | + | In layman's 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. Thus, using real numbers, both multiplication and addition are commutative, and subtraction and division are not. |

− | It is as if the numbers are "commuting" from one place to another. | + | |

The commutative property <strike>implies</strike> does not imply the [[associative property]]. | The commutative property <strike>implies</strike> does not imply the [[associative property]]. | ||

[[Category:Mathematics]] | [[Category:Mathematics]] |

## Revision as of 22:39, 21 April 2011

In mathematics, the **commutative property** states that a binary operation 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 set of real numbers. When a group's operation is commutative, it is said to be abelian.

In layman's 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. Thus, using real numbers, both multiplication and addition are commutative, and subtraction and division are not.

The commutative property ~~implies~~ does not imply the associative property.