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 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. | It is as if the numbers are "commuting" from one place to another. | ||
| − | The commutative property implies the [[associative property]]. | + | The commutative property <strike>implies</strike> does not imply the [[associative property]]. |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 06:02, November 9, 2010
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'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.
The commutative property implies does not imply the associative property.