- #1
gtfitzpatrick
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Homework Statement
prove that R under addition is not isomorphic to[tex] R^*[/tex], the group of non zero real numbers under multiplication.
Homework Equations
The Attempt at a Solution
[tex]\varphi:(R,+) \rightarrow (R^* , .)[/tex]
let [tex]\varphi[/tex](x) = -x
then [tex]\varphi[/tex](x+y) = -(x+y) = -x-y
[tex]\neq \varphi(x)\varphi(y) = (-x)(-y) = xy \neq -x-y[/tex]
since these are not equal it proves they are not isomorphic?
im a little confused about this, am i doing this right?
Thanks all