real analysis – Show set is not Jordan measurable


I have a set consisting of the points of a countably infinite, non-constant sequence on a compact set in $mathbb{R}$. I want to show that this isn’t Jordan measurable, but I am not quite sure how to approach it.

I know that the Bolzano–Weierstrass theorem applies so I know that there is a convergent subsequence. My approach is to try to show that boundary of the set does not have volume $0$ in order to show that the set is not Jordan measurable. However, I am not quite sure how to use the fact that it has convergent subsequence.