Pentashagon comments on On the importance of taking limits: Infinite Spheres of Utility - Less Wrong
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Comments (58)
Does it matter if the number of people is countably infinite, or uncountably infinite?
If each person corresponds on a 1-1 basis with the real numbers, there are an infinite number people who will not be selected to change spheres on any of the integer-numbered days. Those people will never change spheres.
Just compare the cardinality of the number of days to the cardinality of the number of people. If |days| < |people| then start them in the heaven sphere. If |days| = |people| then it doesn't matter (by symmetry the first are last, and the last first, so to speak). If |days| > |people| then start them in the hell sphere.
My first impression was the same as yours, but then I realized there was no guarantee about any of the cardinality, even for the set of days. The post assumes the reals, but comparing the cardinality should work for any sets (although if they're bigger than the reals can we really compare "utility" at all?)
I think that's a better statement of what I tried to say.