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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