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Re: Cantor's Proofs
Posted:
Oct 14, 2011 8:40 PM
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On 2011-10-14, Dick <DBatchelo1@aol.com> wrote:
> Since the conditions for the real numbers does not state the LUB
> property I am entitled to use as counter examples sets that do not
> have this property.
No, the Cantor diagonal proof had nothing directly to do with real
numbers. It concerned the set of all binary sequences of a particular
pair of elements. The corollary that the reals are uncountable
follows from the existence of a simple injection from these into the
reals. If you instead choose some subset of the reals, there may not
exist such an injection.
--
Tim
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