Achilles paradox

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The paradox which arises from considering how overtaking takes place. Achilles gives a tortoise a head start in a race. To overtake, he must reach the tortoise's initial position, then where the tortoise had moved to, and so on * ad infinitum. The conclusion that he cannot overtake because he has to cover an infinite sum of well-defined non-zero distances is false, hence the paradox.

Subjects: Mathematics.

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