Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR:
THE REALS ARE UNCOUNTABLE!

Replies: 47   Last Post: Jan 12, 2013 11:33 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
ross.finlayson@gmail.com

Posts: 918
Registered: 2/15/09
Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!

Posted: Jan 12, 2013 11:23 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Jan 11, 6:40 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <117f2274-de68-4a54-b90d-f3e423c3d...@c16g2000yqi.googlegroups.com>,
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 11 Jan., 10:39, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <3810bc42-c275-4897-94ba-8280508e9...@10g2000yqk.googlegroups.com>,

>

>
> > Correct. But Cantor's list requires decimals or equivalent
> > representations.

>
> Actually, Cantors original list for anti-diagonalization was of
> sequences of letters from {m,w}, not digits, and were not interpreted as
> numbers.
>
>


...

>
> Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben
> können.
>
> No one shall expel us from the Paradise that Cantor has created.
>
> David Hilbert
> --



"That's not "Cantor's original argument", for what he may have first
stated it.

http://en.wikipedia.org/wiki/Cantor's_theorem#History

For subsets M of N, the ordinal indices of S range from zero in alpha
through omega, let f_alpha(M) be onto {0} and f_omega(M) be onto {1},
then, G_alpha(M) = 1 - f_alpha(M) -> {1} = f_omega(M). Here f
satisfies the hypothesis of being a function from N at least into S
and doesn't see the contradiction. Here there are obviously infinite
ordinals between alpha and omega, between which there are functions
from N onto {0,1}. Basically this S has only one of the two values on
the ends, and two in the middle, with symmetry and reflection, and the
ordinal omega would look like 2^omega. Basically for each member of S
from zero, there is a corresponding bit-wise complement, in the same
order, in reverse, from omega, such that G_alpha = f_omega-alpha.
Thusly, G is not: not in S. Then, that would get back into Cantor
himself justifying counting backward from "limit ordinals", or that
omega is simply the next limit ordinal.

For Russell's, let phi-x be or include that "not-phi-x is false",
i.e., truth.

If all the propositions in the language have truth values, and the
theorem is about their self-referential content, then admit their self-
referential statement, here that in the language one, or the other, of
the statement, and its negation, is a statement in the language. "

Adam and Eve might have still been there hadn't they ate from the tree
of knowledge. Hilbert's Programme: completeness.

Regards,

Ross Finlayson




Date Subject Author
1/9/13
Read FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR:
THE REALS ARE UNCOUNTABLE!
Zaljohar@gmail.com
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Zaljohar@gmail.com
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
JT
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
JT
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Zaljohar@gmail.com
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
ross.finlayson@gmail.com
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Zaljohar@gmail.com
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Zaljohar@gmail.com
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Zaljohar@gmail.com
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Zaljohar@gmail.com
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Zaljohar@gmail.com
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Zaljohar@gmail.com
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
ross.finlayson@gmail.com
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/12/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
ross.finlayson@gmail.com
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/10/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/11/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/12/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
ross.finlayson@gmail.com
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
mueckenh@rz.fh-augsburg.de
1/9/13
Read Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Virgil

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.