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Binary operations

by Jumblebee
Tags: binary, operations
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Jumblebee
#1
Jan20-09, 10:09 PM
P: 12
So I have really been struggling with this question. The original question said: The map [tex]\varphi[/tex]:Z->Z defined by [tex]\varphi[/tex](n)=n+1 for n in Z is one to one and onto Z. For (Z, . ) onto (Z,*) (i am using . for usual multiplication) define * and show that * makes phi into an isomorphism.
I know that the operation must be m*n=mn-m-n+2. But I get stuck in proving that the operations are preserved. When I do [tex]\varphi[/tex](m.n) i get mn+1. and i can't get [tex]\varphi[/tex](m). [tex]\varphi[/tex](n) to work. I think I am doing something wrong. Can any one help?
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Jumblebee
#2
Jan20-09, 10:19 PM
P: 12
Never mind! i just got it to work!


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