Re: Countable vs Continuous

From: <>
Date: Fri, 22 Jun 2001 18:50:06 +0200

> 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
Received on Fri Jun 22 2001 - 09:54:07 PDT

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