Please me some clues verifying the following groups are not isomorphic. I 've found this problem interesting.
- $(\mathbb Z,+)$ and $(\mathbb Q,+)$
- $(\mathbb Q,+)$ and $(\mathbb R,+)$
- $(\mathbb Z[x],+)$ and $(\mathbb Q[x],+)$
- $(\mathbb Q[x],+)$ and $(\mathbb Q,+)$
Appreciate your help.