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Valandil said:
I'm ignoring much more. That is one of Zeno's paradoxes, ancient problems of the greeks.
The problem here is actually a misunderstanding of infinites. The series is actually convergent to 1/0, not 0. I don't really want to go over the math here, but suffice to say that my conclusion is totally wrong.
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I'm really interested in knowing what series is "convergent to 1/0" in the Zeno's paradox story. The way I see it, the time series is simply convergent to a finite, non-zero value, which is exactly the time where the arrow (hare) will catch up with the runner (tortoise).