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EquinoctialPie t1_jeb1bbu wrote

The paradox is that you have one line of reasoning that shows that Achilles will never reach the Tortoise, and another line of reasoning that shows that Achilles will eventually reach the Tortoise.

If both lines of reasoning are correct, you get a contradiction. But it's not obvious where the mistake is, hence being called a paradox.

The resolution to this paradox is the realization that an infinite series can have a finite sum. That is, the first line of reasoning shows that it will take an infinite number of steps for Achilles to reach the Tortoise, but since each step gets shorter, it can be done in a finite amount of time.

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quackl11 t1_jecregc wrote

I always thought the soloution was e will pass when his indiviual strides are longer than the tortoises distance traveled during the time it takes Achilles to make one stride

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SYLOH t1_jecutr2 wrote

To complete a stride, Achilles foot would have to move to half way through his stride, and to do that it would need to move half way to that , and so on.
That just shifts the thing down.

The universe having some kind of finite resolution like the planck length would also resolve this.
But it's not necessary, for the reasons stated above.

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