Suppose that the swift Achilles is having a race with a tortoise. Since the tortoise is much slower, she gets a head start. When the tortoise has reached a given point a, Achilles starts. But by the time Achilles reaches a, the tortoise has already moved beyond point a, to point b. And by the time Achilles reaches b the tortoise has already moved a little bit farther along, to point c. Since this process goes on indefinitely, Achilles can never catch up with the tortoise.

How can this be?

Taken from - http://members.aol.com/kiekeben/zeno.html

This is not a paraox because achillies CAN catch up with and indeed overtake the tortoise. One only has to watch a motor race where one of the faster cars starts, say at the back of the grid or near to the back and ends up over taking alot of the slower cars infront of it. even if you define a distance short enough for achilles not to over take it is still not a paradox and is simply a matter of cause. the tortoise had a head start and was close enough to the finish line at the start of the race to make it across before achilles caught up with him.

Posted by ben on 2003-12-10 20:10:49