Let A and B be nonempty compact subsets of $\mathbb{R}^n$ with $A \cap B = \emptyset$, then there exists a $\delta > 0$ such that for all $a \in A$ and $b \in B$, $|a-b| > \delta$.
I can not seem to prove this. I have tried many things and been given many hints with no luck. Can someone show me how this one is done please? Thank you!