Here is a very tricky question that I am trying to solve since last three days but until now I couldn't find the solution. Can anyone be of some help to solve this question?
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Does a binary operation
exist such that
and
are isomorphic? Prove your answer.
NOTE:
is the set of natural numbers,
is the set of integers and + is the addition operation. Two algebraic structures
and
are isomorphic if and only if a bijection
exists such that
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I would appreciate if full proof of this problem can be written
Bundle of thanks in advance.
Regards