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
say the distance between a and b is 80miles, and the distance between b and c is 40 miles, and the distance between c and d is 20 miles... etc.
using this the tortoise will forever be ahead of Achilles, until the limiting point, which in this case is just short of 160. If the finish point is beyond 160, then Achilles will win, therefore: if Achilles will never catch up with the tortoise, the finish must be within the limiting point.
by the way// this uses the ratio of speed 1/2, this number can be substituted and the numbers changed accordingly, 1/2 is simply easier to show.
simple
