Virgil
Posts:
4,491
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 4, 2013 4:30 PM
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In article
<00fe6649-4559-43ed-81d7-0df2b055e787@r14g2000vbd.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 3 Jan., 22:36, Virgil <vir...@ligriv.com> wrote:
>
> > > It is prerequisite when dealing with numbers. And it is exactly what
> > > Cantor applied, He distinguished numbers at finite places.
> >
> > Cantor may have distinguished numerals at finite places, but numerals
>
>
> So Cantor "proved" that there are uncountably many numerals?
Actually, Cantor proved that the set of real numbers was not countable
in the sense that no mapping from N to R can be surjective, which is
what, by definition, being countable requires.
> Why then does anybody believe in uncountably many numbers?
Because counting is provably unable to exhaust them.
Does WM have some definition of countability of a set other than
existence of surjection from N to the set in question?
If so, he should present his alternative ASAP, because as long as that
definition holds, the reals remain provably uncountable.
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