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Topic: UNCOUNTABILITY
Replies: 59   Last Post: Dec 24, 2012 2:06 PM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: UNCOUNTABILITY
Posted: Dec 22, 2012 12:56 PM

On 22 Dez., 06:05, Zuhair <zaljo...@gmail.com> wrote:
> On Dec 21, 8:44 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> Cantor's argument is about diagonalizing any
> COUNTABLE set of reals. So again for any *countable* set S of reals
> there is a diagonal r that differs from each real in S by a finite
> initial segment n(r).

But each of these different initial segments n(r) is contained in
another place of *that* Binary Tree which contains only all finite
paths - hence is countable even in your opinion.

Therefore Cantor's argument here fails in case of an obviously
countable set.

> This has been PROVED by Cantor

not considering the Binary Tree!

> This logically entails that the set R
> of ALL reals cannot be countable,

and that it must be countable.
!
>
> A final word about your project. You tried to prove an "inconsistency"
> with the assumption of uncountability of reals, which you couldn't
> manage to carry out. And nobody managed and nobody could ever manage
> because uncountability of reals is provable in very weak fragments of
> Z actually of second order arithmetic, and those are PROVED to be
> consistent.

From that you can see what a mess your "proofs" are. It's matheology.
No serious person will give a dime for that nonsese.

Regards, WM

Date Subject Author
12/19/12 george
12/20/12 Zaljohar@gmail.com
12/20/12 Barb Knox
12/20/12 ross.finlayson@gmail.com
12/20/12 Zaljohar@gmail.com
12/20/12 ross.finlayson@gmail.com
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/20/12 Graham Cooper
12/20/12 mueckenh@rz.fh-augsburg.de
12/20/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 William Hughes
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/22/12 William Hughes
12/22/12 Graham Cooper
12/23/12 Virgil
12/23/12 William Hughes
12/24/12 Graham Cooper
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 William Hughes
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 Virgil
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/21/12 Virgil
12/20/12 Virgil
12/20/12 Graham Cooper
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 Graham Cooper
12/21/12 Graham Cooper