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## Zeno's İdea

Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.

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Mar 9 2013: Zeno's paradox has fallen apart after infinite series has been discovered. An infinite series can have finite sum, like say 1+1/2+1/4+1/8+1/16+.....infinity = 2. So your statement 'Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.' is neither true mathematically or physically.