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On Tue, Nov 02, 1999 at 05:47:34AM -0800, Bostrom,N (pg) wrote:
> Bruno wrote:
>
> >Juergen Schmidhuber:
>
> >> Even the set of all real #'s is not formally describable.
> You cannot
> >> write a program that lists all reals. In infinite but
> countable time
> >> you can write down a particular computable real, but not
> all reals.
>
> >I don't agree. Indeed, you cannot write a program that
> lists all reals.
> >But in infinite and still countable time you can write down
> all the reals,
> >by dovetailing on all initial segment of all the reals,
> including
> >non computable one.
>
> > 0.0 0.1
> > 0.00 0.01 0.10 0.11
> > 0.000 0.001 0.010 0.011 0.100 0.101 0.110
> 0.111
> > etc. etc.
>
> >There is of course no contradiction with the fact that most
> of the reals
> >are uncomputable, and that the set of reals is uncountable.
>
> No you've got that wrong, Bruno. The output of the process you describe is a
> countable string of reals, and it thus leaves out the vast majority of all
> real numbers. (To see that the string is countable, map it to the integers
> as follows: upper-left=1, upper-right = 2, second row-first column = 3 etc.;
> this mapping will include all entries in your listing) -- What you are
> leaving out are a lot of reals that have an infinite binary decimal
> representations.
>
>
> Nick Bostrom
> Dept. Philosophy, Logic and Scientific Method
> London School of Economics
> Email: n.bostrom.domain.name.hidden <mailto:n.bostrom.domain.name.hidden.ac.uk>
> Homepage: http://www.analytic.org <http://www.analytic.org>
Received on Tue Nov 02 1999 - 06:16:27 PST