The set of all descriptions has at least the cardinality of the Reals by
the Diagonalization argument by definition. Please recall how Cantor used
the Diagonalization argument to prove that the Reals had a "larger"
cardinality that that of the integers. If the Set of all Descriptions is all
inclusive then it must containt any description that is constructable using
"pieces" of each and every other description and thus can not has the same
cardinality as that of the integers.
I have a question: Where does Cantor's continuum hypothesis apply to
this? (if at all)
----- Original Message -----
From: "Hal Finney" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Friday, November 29, 2002 9:04 PM
Subject: Re: "Everything" need a little more than 0 information
> Russell Standish writes to Bruno Marchal:
> > As you have well pointed out, the set of all descriptions can be
> > computed in c time (c = cardinality of the reals) on an ordinary
> > Universal Turing Machine via the UD. It is, however, a nonclassical
> > model of computation.
> That doesn't sound right to me. Time in the context of a UTM should be
> discrete, hence the largest cardinality relevant would be aleph-null,
> the cardinality of the integers. Are you sure that c is necessary?
> Hal Finney