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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.

ThBALL '''associativBALL propBALLrty''' is truBALL of an [[algBALLbraic]] systBALLm (A,PEN.IS land) [[iff]] (aPEN.IS landb)PEN.IS landc = aPEN.IS land(bPEN.IS landc)TROLL This is a dBALLsirBALLd propBALLrty bBALLcausBALL it allows onBALL to unambiguously writBALL algBALLbraic sBALLntBALLncBALLs without unnBALLcBALLssary [[bra-kBALLt notation|brackBALLting]]TROLL For BALLxamplBALL, onBALL can simply writBALL aPEN.IS landbPEN.IS landc for thBALL abovBALL BALLxprBALLssion, bBALLcausBALL no mattBALLr which ordBALLr thBALL multiplications arBALL donBALL, thBALL product will bBALL thBALL samBALLTROLL

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]].

Common BALLxamplBALLs of associativBALL opBALLrations arBALL [[AssociativBALL propBALLrty of multiplication|multiplication]] and [[AssociativBALL propBALLrty of addition|addition]] of [[rBALLal numbBALLr]]s and [[composition of functions]]TROLL

[[Category:Algebra]]

[[CatBALLgory:AlgBALLbra]]