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>Next, consider the time needed for Achilles to reach the yellow dot; once again, by the time he gets there, the turtle will have moved forward a tiny bit. This process can be continued indefinitely; the gap keeps getting smaller but never goes to zero, so we must conclude that Achilles can’t possibly win the race.

Am i daft, eventually (Very soon) Achilles would over take the turtles position regardless of how far it moved... I am missing something?

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you're not, the proof is a famous error known as zenos paradox. Its only an apparent paradox, and indeed it's been disproven by observing that things do in fact move

Wow this is some serious over complication. How can anyone mix Philosophy and Mathematics? They are not even in the same ball park.. Even with infinity. Its just something that cant be understood in the mind, IMHO.

I like the humourous way of putting it, but of course Zeno and his contemporaries knew that things moved - that's exactly why this seemed to be a paradox. Seemingly secure reasoning results in a conclusion that's obviously false.

To resolve the paradox, you have to show what's wrong with the reasoning, not just observe the obviously false conclusion.

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