Difference between revisions of "Associative property"
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| − | + | The '''associative property''' is true of an [[algebraic]] system (A,*) [[iff]] (a*b)*c = a*(b*c). This is a desired property because it allows one to unambiguously write algebraic sentences without unnecessary [[bra-ket notation|bracketing]]. For example, one can simply write a*b*c for the above expression, because no matter which order the multiplications are done, the product will be the same. | |
| − | Common | + | Common examples of associative operations are [[Associative property of multiplication|multiplication]] and [[Associative property of addition|addition]] of [[real number]]s and [[composition of functions]]. |
| − | [[ | + | [[Category:Algebra]] |
Latest revision as of 14:12, November 11, 2011
The associative property is true of an algebraic system (A,*) iff (a*b)*c = a*(b*c). This is a desired property because it allows one to unambiguously write algebraic sentences without unnecessary bracketing. For example, one can simply write a*b*c for the above expression, because no matter which order the multiplications are done, the product will be the same.
Common examples of associative operations are multiplication and addition of real numbers and composition of functions.