Date: Mar 30, 2013 9:37 PM
Subject: Re: Matheology � 224
WM <email@example.com> 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
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
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
> > > > 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.
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
But most of the sequences in a CIBT, even if convergent, are NOT