Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.5
Prove that the additive groups $\mathbb{Q}$ and $\mathbb{R}$ are not isomorphic.
Solution: We know that no bijection $\mathbb{Q} \rightarrow \mathbb{R}$ exists, so no such isomorphism exists.
