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