You have a countable
infinity of balls labelled with the
natural numbers, and an infinitely large urn which starts empty. After
one minute, you put in balls 1 to 10, and remove ball 1. After 1.5 minutes, you put in balls 11 to 20, and remove ball 2. After
1.75 minutes, you put in balls 21 to 30, and remove ball 3. And so on.
After two minutes, how many balls are left in the urn? It seems as though there should be infinitely many, as every time you take
one ball out, you put in another ten. In fact there are zero - ball 1 was removed at step 1 (and never put back in), ball 2 was
removed at step 2, and in general, ball n was removed at step n.