A tortoise and a hare are racing. The tortoise is given a hundred metre head start on the (obviously much speedier) hare. When the tortoise touches the hundred metre line, the hare starts off, thinking to himself that he himself needs to get to the hundred metre line; but when he gets there the tortoise is slightly ahead (a hundred and one metres, say). So the rabbit, as he zooms past the hundred metre line, thinks to himself that now he needs to get to the hundred-and-one metre line. But when he gets there, the tortoise is slightly ahead still! This continues on infinitely, with the hare catching up to where the tortoise *was* only to find him slightly ahead.

Therefore, the hare must go through an infinite number of distances before he can overtake the tortoise. Thus, while common sense and common experience would hold that the rabbit can catch the tortoise, according to the above argument, he cannot. Solve the paradox.