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Topic: Matheology § 190
Replies: 15   Last Post: Jan 14, 2013 3:35 PM

 Messages: [ Previous | Next ]
 ross.finlayson@gmail.com Posts: 643 Registered: 2/15/09
Re: Matheology § 190
Posted: Jan 12, 2013 7:33 PM

On Jan 12, 3:26 pm, Virgil <vir...@ligriv.com> wrote:
> In article
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>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 12 Jan., 22:00, Virgil <vir...@ligriv.com> wrote:
> > > In article

>
> > >  WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > Matheology 190
>
> > > > The Binary Tree can be constructed by aleph_0 finite paths.
>
> > > >         0
> > > >       1, 2
> > > >   3, 4, 5, 6
> > > > 7, ...

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> > > Finite trees can be built having finitely many finite paths.
> > > A Complete Infinite Binary Tree cannot be built with only finite paths,
> > > as none of its paths can be finite.

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> > Then the complete infinite set |N cannot be built with only finite
> > initial segments {1, 2, 3, ..., n} and not with ony finite numbers 1,
> > 2, 3, ...? Like Zuhair you are claiming infinite naturals!

>
> A finite initial segment of |N is not a path in the unary tree |N.
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> And neither |N  as a unary tree nor any Complete Infinite Binary Tree
> has any finite paths.
>
>    "A Complete Infinite Binary Tree cannot be built with only
>    finite paths, as none of its paths can be finite."
>
> Means the same as
>
>    "A Complete Infinite Binary Tree cannot be built HAVING only
>    finite paths, as none of its paths can be finite."
>
> WM has this CRAZY notion that a path in a COMPLETE INFINITE BINARY TREE
> can refer to certain finite sets of nodes.
>
> And no one is claiming any infinite naturals, only infinitely many
> finite naturals.
> --

No, some have infinite naturals.

For example, Boucher's system F or Paris and Kirby's nonstandard
countable naturals, various systems with a point at infinity, from
number theory, others besides your lash-ee have infinite naturals.

No it is not so far-fetched that the naturals are compact, and in
fact, it neatens a variety of facets of their structure.

No, I quite so imagine you two could spew on at each other quite
indefinitely: without much novelty, though it's remarkable that your
mutual esteem and contribution to the discussion would tend to zero.

So, entertain us, that's a request for change. Because, we can quite
well examine your mental fumblings and exhultations in the obvious to
each other, without needing direction in as to the simple segregation
of a man. Plainly don't much care to see you adore him on a pedestal,
nor piss on him down the well. Either extreme is rather repugnant to
the temperant.

No, there's a general interest in sublime facts of the mathematics,
not opinion. And, that deliberation includes notions of infinite
naturals.

Get thee to a scullery, crow.

Regards,

Ross Finlayson