I am trying to prove that the additive groups [itex]\mathbb{Z}[/itex] and [itex]\mathbb{Q}[/itex] are not isomorphic. I know it is not enough to show that there are maps such as, [tex]f:\mathbb{Q}\rightarrow \mathbb{Z}[/itex] where the input of the function, some [itex]f(x=\frac{a}{b})[/itex], will not be in the group of integers because it's obviously coming from rationals. I just don't know how to rigorously prove this, because just because a map is not isomorphic doesn't mean that the whole thing is not isomorphic. Thanks for any help, it is much appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

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# Simple question on disproving a group isomorphism

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