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 Achilles and the Tortoise (Posted on 2002-11-22)
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?

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 See The Solution Submitted by Raveen Rating: 3.0769 (13 votes)

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 no paradox | Comment 20 of 31 |
1/2 + 1/4 + 1/8 ... = 1, a finite number. An infinite sum can be finite with the right parameters. In this case, the sum is finite, so Achilles can overtake the tortoise at that point as long as neither speeds up nor slows down.
 Posted by C.B. on 2003-11-29 19:32:13

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