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.* * *
Universalium. 2010.
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associative law — noun : a law indicating immateriality in the grouping of variables; specifically : any law of the form (φRχ)Rψ=φR(χRψ) where φ, χ, ψ are variables and R a dyadic operator [as (a +b)+c=a+(b+c) in arithmetic or (pvq)vr.≡.pv( … Useful english dictionary
associative law — asociatyvumo dėsnis statusas T sritis automatika atitikmenys: angl. associative law vok. assoziatives Gesetz, n rus. ассоциативный закон, m; сочетательный закон, m pranc. loi d associativité, f ryšiai: sinonimas – jungiamumo dėsnis … Automatikos terminų žodynas
associative law — mathematical law stating that certain operations (addition, subtraction, etc.) may be executed in any sequence without affecting the result … English contemporary dictionary
associative — index apposite, correlative, pertinent Burton s Legal Thesaurus. William C. Burton. 2006 … Law dictionary
Law — /law/, n. 1. Andrew Bonar /bon euhr/, 1858 1923, English statesman, born in Canada: prime minister 1922 23. 2. John, 1671 1729, Scottish financier. 3. William, 1686 1761, English clergyman and devotional writer. * * * I Discipline and profession… … Universalium
Associative property — This article is about associativity in mathematics. For associativity in the central processor unit memory cache, see CPU cache. For associativity in programming languages, see operator associativity. In mathematics, associativity is a property… … Wikipedia
Associative algebra — In mathematics, an associative algebra is a vector space (or more generally, a module) which also allows the multiplication of vectors in a distributive and associative manner. They are thus special algebras. Definition An associative algebra A… … Wikipedia
law — law1 lawlike, adj. /law/, n. 1. the principles and regulations established in a community by some authority and applicable to its people, whether in the form of legislation or of custom and policies recognized and enforced by judicial decision. 2 … Universalium
associative — associatively /euh soh shee ay tiv lee, euh tiv , see /, adv. associativity /euh soh shee euh tiv i tee, see , sheuh tiv /, associativeness, n. /euh soh shee ay tiv, see , sheuh tiv/, adj. 1. pertaining to or resulting from association. 2.… … Universalium
associative — as•so•ci•a•tive [[t]əˈsoʊ ʃiˌeɪ tɪv, si , ʃə tɪv[/t]] adj. 1) pertaining to or resulting from association 2) tending to associate or unite 3) math. pho Math. a) (of an operation on a set of elements) giving an equivalent expression when elements… … From formal English to slang