Does the sum converge on 1 or is it infinite? If it converges on 1, does pausing for a second alter chances of reaching the limit? P.S: this is the progressive dichotomy paradox.
2026-03-26 02:57:58.1774493878
In Zeno of Elea's paradox on the runner, does pausing for a second affect the chances of reaching the limit?
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One reason Zeno's paradox is solvable is that we have a converging series in time as well as distance. Assuming constant speed it takes half the time to cover a 1/4 distance vs a 1/2 distance. If you add a fixed length pause after each step then the total time diverges with infinitely many pauses of length n. For the time of travel to remain finite, you need the pauses to become briefer with each step so that the sum of the paused time converges also.