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Topic: Matheology § 038
Replies: 94   Last Post: Jun 19, 2012 12:56 PM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 038
Posted: Jun 17, 2012 10:17 AM

On 15 Jun., 19:36, Uergil <Uer...@uer.net> wrote:
> In article
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 15 Jun., 01:56, Uergil <Uer...@uer.net> wrote:
> > > In article
> > > <f7304e1b-1ddb-4e44-be50-3ed5d30e3...@d6g2000vbe.googlegroups.com>,

>
> > >  WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > On 14 Jun., 21:59, Uergil <Uer...@uer.net> wrote:
>
> > > > > > > Evidently you misunderstood the question. The question is:
>
> > > > > > Are there uncountably many real numbers.
> > > > > > The answer is a resounding: No.

>
> > > > > Then lets see WM count them!
>
> > > > That cannot be done, because they are not available. It is a
> > > > potentially infinite set. The completely absurd assumption that all
> > > > were "there" (because God knows them) is really ridiculous.

>
> > > > > > No. It is a gross mistake to assume that the rational numbers could be
> > > > > > counted.

>
> > > > > That depends on one's definition of "counting".
>
> > > > No, it depends on the correct understanding of limits.
>
> > > Then WM's definition of 'counting' is grossly different from any
> > > standard meaning in mathemtics.

>
> > > Because by a more standard mathematical definition of counting, the set
> > > of rationals not only CAN be counted it frequently HAS BEEN counted.

>
> > > A Google search for "counting the rationals" came up with 174,000 hits
> > > in 0.61 seconds, including:

>
> > You can do better. Simply try it.
> > Number of angels:
> > 198.000.000 hits in 0.2 s.

>
> Except that many of the "counting the rationals" hits include
> mathematically valid proofs of the countability of the rationals, i.e.
> well-orderings of the rationals that are order-isomorphic to the
> standard well-ordering of the naturals.
>
> Does WM claim that any of those "numberings" of the angels are
> mathematically valid?

With absolute certainty they are not less valid than enumerations of
the rationals.

Date Subject Author
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Uergil
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Uergil
6/14/12 Jürgen R.
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Jürgen R.
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Uergil
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Ki Song
6/14/12 Virgil
6/15/12 mueckenh@rz.fh-augsburg.de
6/15/12 Virgil
6/15/12 mueckenh@rz.fh-augsburg.de
6/15/12 Virgil
6/16/12 mueckenh@rz.fh-augsburg.de
6/16/12 Virgil
6/15/12 mueckenh@rz.fh-augsburg.de
6/15/12 Virgil
6/15/12 Ki Song
6/15/12 mueckenh@rz.fh-augsburg.de
6/15/12 Ki Song
6/15/12 mueckenh@rz.fh-augsburg.de
6/15/12 Ki Song
6/16/12 mueckenh@rz.fh-augsburg.de
6/16/12 Ki Song
6/16/12 mueckenh@rz.fh-augsburg.de
6/16/12 Ki Song
6/17/12 mueckenh@rz.fh-augsburg.de
6/17/12 Ki Song
6/17/12 mueckenh@rz.fh-augsburg.de
6/17/12 Ki Song
6/18/12 mueckenh@rz.fh-augsburg.de
6/18/12 Jürgen R.
6/18/12 mueckenh@rz.fh-augsburg.de
6/18/12 Jürgen R.
6/18/12 mueckenh@rz.fh-augsburg.de
6/18/12 Jürgen R.
6/18/12 Virgil
6/18/12 Virgil
6/17/12 Virgil
6/17/12 YBM
6/17/12 Virgil
6/16/12 Virgil
6/16/12 Virgil
6/16/12 mueckenh@rz.fh-augsburg.de
6/16/12 Virgil
6/17/12 Ki Song
6/17/12 mueckenh@rz.fh-augsburg.de
6/17/12 Ki Song
6/18/12 mueckenh@rz.fh-augsburg.de
6/18/12 Virgil
6/18/12 Virgil
6/18/12 LudovicoVan
6/17/12 Virgil
6/15/12 Ki Song
6/16/12 mueckenh@rz.fh-augsburg.de
6/16/12 Ki Song
6/16/12 mueckenh@rz.fh-augsburg.de
6/16/12 Ki Song
6/17/12 mueckenh@rz.fh-augsburg.de
6/17/12 Ki Song
6/17/12 mueckenh@rz.fh-augsburg.de
6/17/12 Ki Song
6/18/12 mueckenh@rz.fh-augsburg.de
6/18/12 Virgil
6/18/12 mueckenh@rz.fh-augsburg.de
6/18/12 Virgil
6/18/12 mueckenh@rz.fh-augsburg.de
6/18/12 Virgil
6/17/12 Virgil
6/17/12 Virgil
6/16/12 Virgil
6/16/12 Virgil
6/15/12 Virgil
6/15/12 Virgil
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Uergil
6/14/12 Uergil
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Uergil
6/15/12 mueckenh@rz.fh-augsburg.de
6/15/12 Uergil
6/17/12 mueckenh@rz.fh-augsburg.de
6/17/12 Uergil
6/18/12 LudovicoVan
6/18/12 Uergil
6/19/12 mueckenh@rz.fh-augsburg.de
6/19/12 Uergil
6/15/12 Math