(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

for every n in the natural numbers, Vn is a nonempty closed subset of a compact space T. Vn+1 is contained in Vn. Prove the Intersection of all the Vn's from n=1 to infinity does not equal the empty set.

2. Relevant equations

3. The attempt at a solution

This question seems rather easy, actually a little too easy for an advanced topology class. but this is what i did. I tried to prove by contradiction and assume that the Intersection of all the Vn's from n=1 to infinity EQUALS the empty set. By this assumption this would imply that there exists an n in the natural numbers such that that Vn is the empty set. I say this because... for any set A, A n {empty set} = {empty set}. so choosing a Vn to be the empty set would guarantee that the intersection of all the Vn's is the empty set. But this is a contradiction because in the original problem it says for every n in the natural numbers, Vn is NONEMPTY. Is this enough?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proving something is not the empty set

**Physics Forums | Science Articles, Homework Help, Discussion**