I think we can make an even stronger statement: the only way that the usual probability rules (normalizability, additivity) can be satisfied on an infinite sample space is if all but a finite number of simple outcomes have probability zero. — SophistiCat
I can try to give you an example of "an algorithm that gives all integers (without limit) SOME probability of happening" if you like. — flannel jesus
This algorithm is theoretically capable of randomly producing ANY of the infinite sequence of integers, but it preferentially chooses lower numbers. — flannel jesus
I am not sure I understand your algorithm and what probability distribution it gives to the integers — SophistiCat
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