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Notes -
Achilles and the Tortoise isn’t a paradox due to building up something from parts. It’s a paradox due to doing it sloppily.
By analogy, there are various “proofs” that 0 = 1 that rely on bad math, but nobody would argue that the problem is with math. The problem is with people incorrectly using math.
For Achilles, the problem arises because, just as the distance covered gets cut in half, so does the time it takes to cover it.
If it takes you 1 second to cover 1 meter, 0.5 seconds to cover 0.5 meters, etc., the fact that this series never exceeds 2 says you can’t pass 2 meters in less than 2 seconds.
The "paradox" is that Achilles will never pass the tortoise, and "how far can Achilles get in 2 seconds" says nothing meaningful about this.
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