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From: Karl Stiefvater <qarl.domain.name.hidden>

Date: Wed, 30 May 2001 10:29:45 -0500

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

Received on Wed May 30 2001 - 08:38:48 PDT

Date: Wed, 30 May 2001 10:29:45 -0500

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

Received on Wed May 30 2001 - 08:38:48 PDT

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