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Maths Lover
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hi , this proposition is from artin's book ,
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 :)
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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