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Topic: some amateurish opinions on CH
Replies: 57   Last Post: Apr 16, 2013 8:12 PM

 Messages: [ Previous | Next ]
 dan.ms.chaos@gmail.com Posts: 409 Registered: 3/1/08
Re: some amateurish opinions on CH
Posted: Apr 7, 2013 1:06 PM

On Apr 7, 4:04 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 7 Apr., 10:54, fom <fomJ...@nyms.net> wrote:
>
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>
>
>
>
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> > When I failed to complete my education in
> > mathematics, there had been little hope
> > of any professional position.  Whatever
> > mathematical interests I might have chosen
> > to pursue were not dictated on the basis
> > of what would be beneficial to a
> > professional status.

>
> > I had some tangential interest in the
> > continuum hypothesis.  I also believed
> > that the resolution to the continuum
> > hypothesis might be obtained by considering
> > how the sign of equality is used.

>
> > It would be a mistake to think that I
> > did not know what was involved with
> > such a topic.

>
> Be sure, you did not know!
> There is no finished infinity, no uncountability and therefore there
> is no CH!
>
> Regards, WM

There is , at least such a thing as "relative unaccountability" .
You can't enumerate the contents of an infinite integer list :
1 , 0 , 1 , 0 , 1 ......

There's always the "...." left out .
However , you can unambiguously describe the infinite list by finite
wording :

"an integer on the list has :
Value 1 if it's on an 'even position on the list' .
Value 0 if it's on an 'odd position on the list' .

This finite description unambiguously captures my 'infinite list' .
Now , let's say I have a "countable list" of all integer sequences you
could ever think off .

The point is, you can't think of a bijection between that list and N .
This list appears uncountable to you , because it already contains
every integer sequence you could ever think about . You'd run out of
thoughts before you manage to construct an enumeration of my list .

Date Subject Author
4/7/13 fom
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Bergholt Stuttley Johnson
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Virgil
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 Virgil
4/8/13 Virgil
4/9/13 apoorv
4/8/13 Virgil
4/7/13 Virgil
4/9/13 Guest
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 Guest
4/10/13 dan.ms.chaos@gmail.com
4/10/13 fom
4/10/13 JT
4/11/13 apoorv
4/11/13 dan.ms.chaos@gmail.com
4/11/13 apoorv
4/11/13 fom
4/15/13 apoorv
4/15/13 fom
4/16/13 Shmuel (Seymour J.) Metz
4/16/13 fom
4/7/13 Virgil
4/7/13 William Elliot
4/7/13 fom
4/7/13 fom
4/8/13 William Elliot
4/8/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/9/13 fom