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 paradox doesn't take into account that Achilles' one step is probably larger than the tortise's, and so him "reaching" a certain point can mean he steps further than that point. In that case, he might not "catch up" to the exact point the tortoise is but step past it and beat him.

That's more of a common sense-thinking solution, I don't know how to explain it mathematically though!

Posted by sach on 2002-12-10 10:49:32