Hi, I am reading "mathematical analysis" by Apostol right now for a course in analysis. Since I am trying to understand the author's proof of the above theorem(3.25 in the book), but I have something that I can't understand. He assumes that each of the nested sets contains infinitely many points, "...otherwise, the proof is trivial". I can't see why it's trivial and how to prove it. I would be grateful to understand why an infinite intersection of finite sets is non-empty. Thank you.