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 set of [[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 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). 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. | + | 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. For [[vector]]s, the dot product is commutative, while the cross product is not. |
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 15:01, January 25, 2012
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. For vectors, the dot product is commutative, while the cross product is not.
The commutative property implies does not imply the associative property.
