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I'm not sure if I understand the problem. The tortoise walks a foot, and then Achilles stretches the band three feet? If the tortoise doesn't move when the band is stretched, it will never reach the flower. Every foot that it moves results in it then losing two feet. The tortoise is essentially moving backwards.
If the tortoise does move with the band, how much does it move?
I thought the Zeno problem was more like -- the tortoise moves halfway towards Achilles, then half of the remaining distance, then half of the... and so on. So that technically, the tortoise will never get the flower. Although he should be close enough for all practical purposes before long.
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