Stephen Paul King writes:
> 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.

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That would be true IF you include descriptions that are infinitely long.
Then the set of all descriptions would be of cardinality c. If your
definition of a description implies that each one must be finite, then the
set of all of them would have cardinality aleph-zero.
What Russell wrote was that the set of all descriptions could be computed
in c time on an ordinary Universal Turing Machine. My question is, does
it make sense to speak of a machine computing for c steps; it seems like
asking for the "c"th integer.
> I have a question: Where does Cantor's continuum hypothesis apply to
> this? (if at all)
This is the hypothesis that there is no transfinite cardinal between
aleph-zero and c, and I don't see any relevance to it.
Hal