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

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Matheology � 233
Posted: Mar 31, 2013 11:30 AM
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In article
<17e6599f-5537-449a-b4aa-bb1764a3c328@g8g2000vbf.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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?


This is an equally valid question: What's the difference between a duck?
--





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