I remember one of my undergraduate tutors telling me about this paradox, of which I have just been reminded by Littlewood's Miscellany.
At one minute to noon the numbers 1 to 10 are put into a box, and the number 1 is removed.
At 1/2 minute to noon the numbers 11 to 20 are added to the box, and 2 is removed.
At 1/3 minute to noon the numbers 21 to 30 are added to the box, and 3 is removed.
And so on.
How many numbers are in the box at noon? The answer is obviously 9+9+9+9+... which looks as if it should be infinite. But in fact there are no numbers in the box, because if you suggest that number n might be there, I point out that it was taken out at 1/n of a minute before noon. The box is empty: nine times infinity is zero.
One has to be careful in dealing with infinity!