Intersection of Open Nested Sets which is Empty

Put a_n = (0, 1/n), then a_(n+1) is a subset of a_n for each n >= 1.

Now set I = int(a_n, n = 1, 2, 3,...).

If I is not empty, there is x in I, so x is in a_n for each n, so 0 < x < 1/n for each n. By the squeeze principle x = 0, a contradiction.

Someone asked me this a while ago and this is the answer I gave them. The whole point of this is that if the a_n's where closed and bounded and nested, the intersection would be nonempty.