> O O > ??? - There is no way of assigning equal
> OO O O O > nonvanishing probability to infinitely
> O O O O > many mathematical structures, each being
> O O O > represented by a finite set of axioms.
> OO O O O
> O okay - strictly speaking, you are correct. but a
> OOOOOOO common trick is to compute equal-probabilities
> O on finite subsets of the infinite set. and then
> O OOOOO O you can take the limit as those subsets "grow"
> O O O to the size of the infinite set.
> OOO O
> O OO the "growing" here is important - very often the
> O OO O order in which you add members to the set change
> O OOOO how the series converges. but for the case of
> O OOO expected complexity, it does not.

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but in the limit uniform probabilities vanish. Maybe you'd like to
write down formally what you mean.