Suppose that H is a closed bounded set of real numbers and that (U sub n) is an expanding sequence of open sets.

(a) Explain why the sequence of sets H \ (U sub n) is a contracting sequence of closed bounded sets.

(b) Use the Cantor intersection theorem to deduce that if H \ (U sub n) does not equal an empty set for every n, then the intersection from n=1 to infinity, of (H \ (U sub n)) does not equal an empty set.