associative law

associative law
Two closely related laws of number operations.

In symbols, they are stated: a + (b + c) = (a + b) + c, and a(bc) = (ab)c. Stated in words: The terms or factors may be associated in any way desired and the result will be the same. This holds for the numbers generally encountered: positive and negative, integral and fractional, rational and irrational, real and imaginary. Exceptions occur (e.g., in nonassociative algebras and divergent infinite series). See also commutative law, distributive law.

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      in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + (b + c) = (a + b) + c, and a(bc) = (ab)c; that is, the terms or factors may be associated in any way desired. While associativity holds for ordinary arithmetic with real or imaginary numbers, there are certain applications—such as nonassociative algebras—in which it does not hold. See also commutative law; distributive law.

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Universalium. 2010.

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