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

Because of your definition, that's why. The limit to this infinite problem is the point at which rabbit actually catches up to hair. It's kinda like traveling on a line segment, but only going a certain percentage, then going that same percentage of the remainder. You'd never get to the end of the line segment, but the end exists. There are a theoretical infinite number of points.

Posted by Lawrence on 2003-08-29 01:19:31