
Re: Matheology § 190
Posted:
Jan 12, 2013 7:33 PM


On Jan 12, 3:26 pm, Virgil <vir...@ligriv.com> wrote: > In article > <4bffb7f39bfa4dae9108da5e24389...@f4g2000yqh.googlegroups.com>, > > > > > > > > > > WM <mueck...@rz.fhaugsburg.de> wrote: > > On 12 Jan., 22:00, Virgil <vir...@ligriv.com> wrote: > > > In article > > > <c061586061904c10918578ed2f6a2...@x10g2000yqx.googlegroups.com>, > > > > WM <mueck...@rz.fhaugsburg.de> wrote: > > > > Matheology 190 > > > > > The Binary Tree can be constructed by aleph_0 finite paths. > > > > > 0 > > > > 1, 2 > > > > 3, 4, 5, 6 > > > > 7, ... > > > > 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. > > > 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. > > 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 lashee have infinite naturals.
No it is not so farfetched 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

