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

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mueckenh@rz.fh-augsburg.de

Posts: 15,083
Registered: 1/29/05
Re: Matheology § 233
Posted: Mar 31, 2013 4:31 AM
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On 31 Mrz., 02:56, Virgil <vir...@ligriv.com> wrote:
> In article
> <2bc13fff-5cbb-43dd-a06a-218c68c99...@m9g2000vbc.googlegroups.com>,
>
>
>
>
>
>  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
added to the list.

> 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



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