> 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/
