> or continous. Don't the computable numbers form a continuum; hence even
> restricting the universe to one we can describe would still allow it to be
> continuous?
>
> Brent Meeker
No, the computable numbers do not form a continuum - there are not more
than countably many of them. Any real number computable in the limit
(such as Pi) has a finite nonhalting program; the set of all such programs
cannot have higher cardinality than the integers.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
Received on Fri Jun 22 2001 - 09:54:07 PDT