- #1

mr.tea

- 102

- 12

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.