Achilles’ Torch
This
paradox combines the Paradox of Dichotomy with the Paradox of the Parity of
Infinity.
Achilles,
swiftest of mortals, opens the Olympic Games by bringing a torch to light the
Olympic flame. Unfortunately he is too swift for his torch, and it flickers due
to the speed of his passage. For the first 1/2 stadia of his run, his torch is
lit; for the next 1/4 stadia of his run, it is out; ; for the next 1/6 stadia,
it is lit; for the next 1/16, it is out; and so on indefinitely.
Achilles’
torch flickers infinitely many times by the time he reaches the Olympic flame.
By that time, is his torch lit or out?
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