We know we can biject the segments of size 0.5, 0.25, 0.125, … to the segments of size 0.25, 0.125, 0.0625, …, furthermore we can biject these segments to the segments of size 0.125, 0.0625, 0.03125, …, and there is no end to it. So, we can use index #1 for segment 0.5. We can as well use index #1 for segment 0.25 or segment 0.125 and so on, since we know there are always infinitely many more segments following. If we create the task:(adsbygoogle = window.adsbygoogle || []).push({});

t = 0: move pen from 0 to 0.5 (taking 1/2 second), naming it segment #1

t = 0.5: move pen from 0.5 to 0.75 (taking 1/4 second), naming it segment #1

t = 0.75: move pen from 0.75 to 0.875 (taking 1/8 second), naming it segment #1

t = 0.875: move pen from 0.875 to 0.9375 (taking 1/16 second), naming it segment #1

…

At which step should we stop using #1 as the segment's index in order to have enough segments of non-zero size left to assign the rest of the natural numbers?

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# Dichotomy paradox reverse engineering

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