Date: Jan 12, 2013 7:33 PM Author: ross.finlayson@gmail.com Subject: Re: Matheology § 190 On Jan 12, 3:26 pm, Virgil <vir...@ligriv.com> wrote:

> In article

> <4bffb7f3-9bfa-4dae-9108-da5e24389...@f4g2000yqh.googlegroups.com>,

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> WM <mueck...@rz.fh-augsburg.de> wrote:

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

> > > In article

> > > <c0615860-6190-4c10-9185-78ed2f6a2...@x10g2000yqx.googlegroups.com>,

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> > > WM <mueck...@rz.fh-augsburg.de> wrote:

> > > > Matheology 190

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> > > > The Binary Tree can be constructed by aleph_0 finite paths.

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> > > > 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.

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> "A Complete Infinite Binary Tree cannot be built with only

> finite paths, as none of its paths can be finite."

>

> Means the same as

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> "A Complete Infinite Binary Tree cannot be built HAVING only

> finite paths, as none of its paths can be finite."

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> 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