Post #712300
2026-03-17 07:56 UTC
#ThisWeeksFiddler, 20260313
This week the #puzzle is: Can You or “Cantor” You Find the Distance? #probabilities #infinity #coding #montecarlo #permutations #distance I start with a number line from 0 to 1, and then I remove the middle third. Then I take each of my remaining pieces (the segment from 0 to 1/3 and the segment from 2/3 […]
https://stuff.ommadawn.dk/2026/03/17/thisweeksfiddler-20260313/
Replies (1)
-
@aleph_omega_plus_four@mastodon.world 2026-03-18 10:34
@LiseAndreasen@mastodon.world let a and b be the two random numbers on the Cantor set and assume without loss of generality that a <= b. Divide into cases according to which ternary digit is the first to differ. In 1/2^n cases, that digit is the nth (there is a 1/2 chance that the first pair is the same, 1/2 that the second is, and so on, and finally we have a 1/2 chance that the nth pair differs). In that case, the difference truncated at the nth digit is 2/3^n,