hi , this proposition is from artin's book ,(adsbygoogle = window.adsbygoogle || []).push({});

it says :

Proposition : suppose an associative law of composition is given on a set S.

There is a unique way to define , for every integer n , a product of n elements

a1, …… , an of S ( we denote it by [a1 …an ] ) with the following properties :

-The product [a1] of one element is the element itself

-The product [a1 a2] of two elements is given by the law of composition ;

-For any integer I between 1 and n , [a1 .. an]=[a1….ai][a(i+1)…..an]

and I didn't understand excatly the meaning which the proposition says , so can anyone make it clear to me please ? and if there an example it'll be more better :)

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# What is the meanning of this propisition ?

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