```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,--
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