Date: Mar 30, 2013 9:37 PM Author: Virgil Subject: Re: Matheology � 224 In article

<1ca524f9-9057-4949-b68d-fcdda479188f@fn10g2000vbb.googlegroups.com>,

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

> On 30 Mrz., 19:03, Virgil <vir...@ligriv.com> wrote:

> > In article

> > <050b4a95-d2b0-433b-98b6-d63c34635...@m9g2000vbc.googlegroups.com>,

> >

> >

> >

> >

> >

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

> > > On 29 Mrz., 19:40, Virgil <vir...@ligriv.com> wrote:

> > > > In article

> > > > <ce3c22f2-9116-4621-b3b4-e722fe51a...@a14g2000vbm.googlegroups.com>,

> >

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

> > > > > On 26 Mrz., 22:47, Virgil <vir...@ligriv.com> wrote:

> >

> > > > > > But a tree that contains paths for all binary rationals will

> > > > > > contain a

> > > > > > path for all limits of a sequences of binary rationals.

> >

> > > > > Does a sequence always contain its limit?

> >

> > > > Depends on the sequence, of course. but a sequence of paths in a

> > > > Complete Infinite Binary Tree in which the nth path must share at least

> > > > n nodes with each of its successors will always converge, though not

> > > > neccessarily to a binary rational.

> >

> > > A sequence of numbers may converge, but not necessarily to a limit

> > > that is a term of the sequence.

> >

> > Precisely my point!

>

> Precisely not your point.

It is still my point, even though clearly WM does not understand it.

> The infinite path is not in the infinite

> sequence of finite paths which are used to construct the complete

> tree.

Each node of the infinite limit path is in all but finitely many of the

infinite sequence of infinite but binary-rational paths of which is a

limit.

otherwise that path would not be a limit or the tree would not be a CIBT.

> >

> > > A sequence of paths may converge, but not necessarily to a limit that

> > > is a term of the sequence.

> >

> > So WM acknowledges that A sequence of binary rational paths can converge

> > to a path that is not a binary rational

>

> and that is not in the tree of all binary rationals.

A tree having all binary rationals AS INFINITE PATHS is the only sort

that can be a CIBT. So whatever sort of trees WM is talking about they

cannot be Complete Infinite Binary Trees.

> >

> >

> >

> > > In mathematics more precision is required.

> >

> > Certainly more than WM is capable of producing,.

>

> You intermingle the paths of the tree and the limits which are neither

> paths nor belong to the tree.

In CIBTs all paths are infinite, so WM must be talking about other types

of trees

> >

> >

> > > > In a COMPLETE INFINITE BINARY TREE, all paths are actually infinite

> > > > --

> >

> > > This is again a simple statement of countermathematical belief

> >

> > It is matter of simple definition.

>

> No.

YES!

WM does not get to decide what can be or cannot be a definition.

> >

> > The definition of a COMPLETE Infinite Binary Tree requires that no path

> > in such a tree can terminate.

>

> An infinite sequence does not terminate. Nevertheless its limit is in

> general not in the sequence. Correct or not?

If they are sequences of paths in a Complete Infinite Binary Tree which

There are a lot of infinite sequences that are "eventually constant" in

a CIBT if one identifies each path with an infinite sequence of 0's and

1's in the binary representations of numbers in [0,1], and those

sequences which are eventually all 0's, and only those, are "eventually

constant".

But most of the sequences in a CIBT, even if convergent, are NOT

eventually constant,

--