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The quickest one will never overtake the slowest one: Zeno’s paradox of Achille and the tortoise

The quickest one will never overtake the slowest one: Zeno’s paradox of Achille and the tortoise The quickest one will never overtake the slowest one: Zeno’s paradox of Achille and the tortoise
Source: Martin Grandjean via Wikipedia
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In the paradox of Achilles and the tortoise, imagine Achilles chasing a tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Supposing that each racer starts running at some constant speed (Achille being very fast, at 1m/S, and the tortoise begin very slow, at 0,1m/s). Before Achilles can catch the tortoise, he will have run 100 meters, bringing Achilles where the tortoise started. But during the time he takes to do this, the tortoise has crawled a much shorter distance, but still, the tortoise has moved forward, by 10 meters. So next Achilles must reach this new point. It will take Achilles some further time to run that distance, during which time the tortoise will have advanced a tiny bit further.

And so on to infinity: every time that Achilles reaches the place where the tortoise was, the tortoise has had enough time to get a little bit further, and so Achilles has another run to make, and so Achilles has an infinite number of finite catch-ups to do before he can catch the tortoise, and so, Zeno concludes, he never catches the tortoise.

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