```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 infinitesequence of finite paths which are used to construct the completetree.>> > 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 rationaland 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 neitherpaths 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 ingeneral not in the sequence. Correct or not? Different in the tree? Ornot? And if so, why?Regards, WM
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