  Before S reaches p2, S must  first reach the point half way between p0 and  p2, namely p3. Again, before  S reaches p3, S must first  reach the point half way between p0 and  p3, namely p4. There is a  half way point again to be reached between p0 and p4. In fact, there is always another half way  point that must be reached before reaching any given half way point,  so that the number of half way points that must be reached between  any pn and any pn-1 is  unlimited. But it is impossible for S to reach an unlimited  number of half way points within a limited amount of time. Therefore, it is impossible for S to traverse the stadium or, indeed,  for S to move at all; in general, it is impossible to move  from one place to another.