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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: 15,238
Registered: 1/29/05
Re: Matheology § 233
Posted: Mar 31, 2013 11:47 AM
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On 31 Mrz., 17:30, Virgil <vir...@ligriv.com> wrote:
> In article
> <17e6599f-5537-449a-b4aa-bb1764a3c...@g8g2000vbf.googlegroups.com>,
>
>
>
>
>
>  WM <mueck...@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?


From the standpoint of matheology, perhaps. Did you hitherto respond
in an unreasonable way because you misunderstood the question?

In mathematics, in particular in analysis, we have ficed rules to
answer such an easy question and to calculate (instead of believing)
the limit.

See Matheology § 234.

Regards, WM



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