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Topic: Matheology � 233
Replies: 37   Last Post: May 12, 2014 10:24 AM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 233
Posted: Mar 31, 2013 4:31 AM

On 31 Mrz., 02:56, Virgil <vir...@ligriv.com> wrote:
> In article
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 30 Mrz., 22:11, Virgil <vir...@ligriv.com> wrote:
>
> > > > > Thus there is always at least one bit of any listed entry disagreeing
> > > > > with the antidiagonanl, just as the Cantor proof requires.

>
> > > > In a list containing every rational: Is there always, i.e., up to
> > > > every digit, an infinite set of paths identical with the anti-
> > > > diagonal? Yes or no?

>
> > > The set of paths in any Complete Infinite Binary Tree which agree with
> > > any particular path up to its nth node is equinumerous with the set of
> > > all paths in the entire tree i.e., is uncountably infinite.

>
> > This was the question: In a list containing every rational: Is there
> > always, i.e., up to every digit, an infinite set of paths identical
> > with the anti-diagonal? Yes or no?

>
> Lists and trees are different. And anti-diagonals derive from lists, not
> trees.
> The entries in  list are well ordered.
> The entries in a Complete Infinite Binary Tree are densely ordered.

The entries in form of nodes are well ordered. Anything else is not

> Those order types are incompatible.

This was the question: In a list containing every rational: Is there
always, i.e., up to every digit, an infinite set of paths (rational
numbers) identical with the anti-diagonal? Yes or no?

Regards, WM

Date Subject Author
3/27/13 Virgil
3/28/13 mueckenh@rz.fh-augsburg.de
3/28/13 fom
3/28/13 fom
3/28/13 fom
3/28/13 rt servo
3/28/13 fom
3/28/13 fom
3/28/13 Virgil
3/28/13 fom
3/30/13 mueckenh@rz.fh-augsburg.de
3/30/13 fom
3/30/13 ross.finlayson@gmail.com
3/30/13 Virgil
3/30/13 Virgil
3/30/13 mueckenh@rz.fh-augsburg.de
3/30/13 Virgil
3/30/13 ross.finlayson@gmail.com
3/31/13 Virgil
3/30/13 fom
5/12/14 ross.finlayson@gmail.com
3/31/13 mueckenh@rz.fh-augsburg.de
3/31/13 fom
3/31/13 Virgil
3/31/13 mueckenh@rz.fh-augsburg.de
3/31/13 fom
3/31/13 Virgil
4/1/13 mueckenh@rz.fh-augsburg.de
4/1/13 fom
4/1/13 Virgil
4/1/13 mueckenh@rz.fh-augsburg.de
4/1/13 Virgil
4/2/13 mueckenh@rz.fh-augsburg.de
4/2/13 Virgil
3/27/13 fom