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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(In reply to Why is this a paradox? by Adam Champken)

Adam, it is not even a paradox mathematically.
As Chris used the term 'time frame', there is no reason why Achilles could catch up with the Tortoise, as if his segments are spaced as shown (one half of the other), it takes him half as long to complete each segment as he took to complete the last segment.

The distance is finite. Let the distance be 1.
Speed = Distance / Time:
Segment 1: 1 = (1/2) / (1/2)
Segment 2: 1 = (1/4) / (1/4)
Segment 3: 1 = (1/8) / (1/8)
Segment 4: 1 = (1/16) / (1/16)
...
Segment n: 1 = (1/(2^n)) / (1/(2^n))

Here, we can see that Achilles retains a constant speed.
We can consider the entire track as one segment, and as Time = Distance / Speed:

Time = 1 / 1
= 1
The time taken is finite.

Posted by Berry on 2003-05-10 03:00:41