Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Objection to Cantor's First Proof
Posted:
Jul 31, 2012 10:56 PM
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In article
<cef3510f-6eca-4e42-9bbe-341b3aa31e0a@id7g2000pbc.googlegroups.com>,
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:
> On Jul 31, 12:48 pm, Virgil <vir...@ligriv.com> wrote:
> > In article <jv8mt2$ok...@speranza.aioe.org>,
> >
> > "LudovicoVan" <ju...@diegidio.name> wrote:
> > > > I'll state the main point again: my counter-argument works either with
> > > > an
> > > > enumeration from N to R (supposedly, the original Cantorian setting),
> > > > or
> > > > with an enumeration from N* to R*. The reason why Cantor's First Proof
> > > > fails is because of invalid reasoning with putative sequences from N to
> > > > R*
> > > > (so that an a_oo looks like it is missing from the enumeration).
> >
> > > That's wrongly put: the point just boils down to the fact that, to
> > > consider
> > > a_oo as a real number that belongs or does not belong to (x_n), we need
> > > consider sequences over N*.
> >
> > You may need to but those who are basing their analysis on standard
> > mathematics do not.
> >
> > It is well known in standard mathematics that a nested sequence of real
> > intervals, with each being a proper subinterval of all its predecessors,
> > has a non-empty intersection, which may be an interval of positive
> > length, in which case your alleged a_oo is a real an interval of
> > positive length.
> > --
> >
> >
>
>
> Huh, well how exactly the opposite that is to what you wrote before.
>
Actually not at all different from what wrote before.
But what I wrote seems to be quite different from what you claim to have
read.
--
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