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Topic: Objection to Cantor's First Proof
Replies: 107   Last Post: Sep 6, 2012 5:16 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 4,482 Registered: 1/6/11
Re: Objection to Cantor's First Proof
Posted: Jul 31, 2012 10:56 PM

In article
"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
--

Date Subject Author
7/24/12 LudovicoVan
7/24/12 LudovicoVan
7/24/12 LudovicoVan
7/24/12 LudovicoVan
7/25/12 Virgil
7/26/12 LudovicoVan
7/26/12 Virgil
7/26/12 LudovicoVan
7/26/12 Virgil
7/27/12 LudovicoVan
7/27/12 Mike Terry
7/27/12 LudovicoVan
7/28/12 Virgil
7/28/12 Mike Terry
7/28/12 LudovicoVan
7/28/12 Virgil
7/28/12 Virgil
7/28/12 Virgil
7/29/12 Shmuel (Seymour J.) Metz
7/25/12 David C. Ullrich
7/26/12 LudovicoVan
7/26/12 Shmuel (Seymour J.) Metz
7/26/12 Gus Gassmann
7/26/12 LudovicoVan
7/26/12 Gus Gassmann
7/26/12 LudovicoVan
7/26/12 LudovicoVan
7/26/12 gus gassmann
7/26/12 David C. Ullrich
7/26/12 Shmuel (Seymour J.) Metz
7/26/12 LudovicoVan
7/27/12 Frederick Williams
7/27/12 Jesse F. Hughes
7/27/12 Frederick Williams
7/27/12 dilettante
7/27/12 David C. Ullrich
7/27/12 gus gassmann
7/27/12 Frederick Williams
7/27/12 dilettante
7/29/12 Shmuel (Seymour J.) Metz
8/9/12 Pubkeybreaker
8/9/12 LudovicoVan
7/26/12 Shmuel (Seymour J.) Metz
7/26/12 LudovicoVan
7/25/12 Shmuel (Seymour J.) Metz
7/28/12 LudovicoVan
7/28/12 Virgil
7/28/12 Mike Terry
7/28/12 ross.finlayson@gmail.com
7/28/12 LudovicoVan
7/28/12 ross.finlayson@gmail.com
7/28/12 Virgil
7/29/12 ross.finlayson@gmail.com
7/29/12 Virgil
7/30/12 LudovicoVan
7/30/12 Virgil
7/30/12 ross.finlayson@gmail.com
7/30/12 Virgil
7/30/12 ross.finlayson@gmail.com
7/31/12 Virgil
7/28/12 LudovicoVan
7/28/12 Virgil
7/29/12 David C. Ullrich
7/30/12 LudovicoVan
7/30/12 Virgil
7/29/12 David C. Ullrich
7/30/12 LudovicoVan
7/30/12 Shmuel (Seymour J.) Metz
7/30/12 David C. Ullrich
7/30/12 Virgil
7/31/12 LudovicoVan
7/31/12 LudovicoVan
7/31/12 Virgil
7/31/12 LudovicoVan
7/31/12 Virgil
7/31/12 ross.finlayson@gmail.com
7/31/12 Virgil
7/31/12 William Hughes
8/1/12 Shmuel (Seymour J.) Metz
7/31/12 Virgil
7/31/12 ross.finlayson@gmail.com
7/31/12 Virgil
8/1/12 ross.finlayson@gmail.com
8/2/12 Virgil
8/9/12 Pubkeybreaker
9/6/12 ross.finlayson@gmail.com
8/1/12 LudovicoVan
8/1/12 Jim Burns
8/1/12 LudovicoVan
8/1/12 William Hughes
8/1/12 LudovicoVan
8/1/12 William Hughes
8/1/12 Virgil
8/1/12 Jim Burns
8/1/12 LudovicoVan
8/1/12 LudovicoVan
8/2/12 Jim Burns
8/2/12 Virgil
8/1/12 Virgil
8/1/12 hagman
8/1/12 LudovicoVan
8/2/12 Virgil
8/2/12 Shmuel (Seymour J.) Metz
8/3/12 ross.finlayson@gmail.com
8/2/12 David C. Ullrich
8/1/12 Virgil
7/29/12 Shmuel (Seymour J.) Metz
7/30/12 Marshall