aha! thank you for replying. i'll say more when
OOO O O i get a moment, but let me first clean-up my
O OO O sloppy language:
OO O O
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.
O O OO
O O
O OOOO O
O -k