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Re: Cantor's Proofs
Posted:
Oct 18, 2011 9:34 PM
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On 2011-10-16, Dick <DBatchelo1@aol.com> wrote:
> The topic of Cantor's Second proof always raises a great deal of
> interest. Unfortunately, it also raises a great deal of heat. I think
> this is largely caused by the limited vocabulary available to those
> taking the "classical" view.
No, this is rubbish. That's what casues most of the heat: people post
nonsense and get annoyed when corrected.
> Coming from recursive function theory I can say "The set of computable
> reals is not recursively-enumerable but is Goedelizable." Tjis, I
> think is clear. Things are much more difficult for the classisist. The
> only words available are "enumerable" and "uncountable." He ants to
> say that the computable reals cannot be listed but are enumerable
In classical mathematics the computable reals can be listed.
Obviously. Cantor's 2nd proof shows that the set of *all* reals (or
more precisely a set of all binary sequences) that cannot be listed.
Vocabulary has nothing to do with it, and furthermore computability
and recursion are perfectly valid and common terms in classical
mathematics.
--
Tim
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