Date: Mar 30, 2013 6:41 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
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. The infinite path is not in the infinite

sequence of finite paths which are used to construct the complete

tree.

>

> > 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.

>

>

>

> > 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 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.

>

> 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? Different in the tree? Or

not? And if so, why?

Regards, WM