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Seek_Equilibrium t1_jcbheol wrote

Reply to comment by throwawayski2 in A philosophical dive into “Everything Everywhere All at Once” by Azmisov

> But if you talk about proportions or the probability of choosing an element from a given subset (what I suppose you actually mean by frequency), then this is exactly the way you define these things in Mathematics when dealing with infinite sets.

The phrase “from a given subset” is catching my attention. Are you talking about defining a probability measure on a finite subset of an infinite set? Because if so, that of course wouldn’t bear on the core issue being discussed of whether and how a unique probability distribution could be defined over an entire infinite set - but I am probably missing what you’re truly aiming at so maybe you can clarify.

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throwawayski2 t1_jccd2r6 wrote

No, it can also be defined on infinite subsets. That's why I mentioned Cantor sets, because these are measurable uncountable sets, such that choosing an element from it (given uniform choice from the bounded set on which it is defined) has probability 0 (which is different from our finite intuition, that it is impossible).

It is basically just a generalization of the concept of volume.

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