Date: Mar 30, 2013 2:03 PM
Subject: Re: Matheology � 224
WM <firstname.lastname@example.org> 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!
> 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.
> In mathematics more precision is required.
Certainly more than WM is capable of producing,.
> > 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.
The definition of a COMPLETE Infinite Binary Tree requires that no path
in such a tree can terminate.
At least it does so everywhere outside of Wolkenmuekenheim,