Date: Feb 3, 2013 3:57 PM
Author: Virgil
Subject: Re: Matheology � 203
In article

<b534045b-5f20-41de-9ddd-98017f91892a@l9g2000yqp.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 3 Feb., 00:22, William Hughes <wpihug...@gmail.com> wrote:

> > On Feb 2, 11:58 pm, William Hughes <wpihug...@gmail.com> wrote:

> >

> >

> >

> >

> >

> > > On Feb 2, 11:42 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> >

> > > > On 2 Feb., 23:36, William Hughes <wpihug...@gmail.com> wrote:

> >

> > > > > On Feb 2, 11:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> >

> > > > > > On 2 Feb., 20:11, William Hughes <wpihug...@gmail.com> wrote:

> >

> > > > > > > > > > > Can a potentially infinite list

> > > > > > > > > > > of potentially infinite 0/1

> > > > > > > > > > > sequences have the property that

> > > > > > > > > > > if s is a potentially infinite 0/1

> > > > > > > > > > > sequence, then s is a line of L

> >

> > > > > <snip>

> > > > > > For every s: There is alsways a list that contains the first n bits

> > > > > > of

> > > > > > s.

> >

> > > > > Is there a single line which contains s

> > > > > Yes or no

> >

> > > <snip>

> >

> > > > There is no complete s.

> >

> > > Then the answer is no

> >

> > Indeed, since there is no single line, l,

> > such that every initial segment of s is contained

> > in l, we do not even have to talk about complete s.-

>

> In fact we can say that in a suitable list "every" initial segment of

> s is contained in some line, since there is no s(n) = (s1, s2, ...,

> sn) missing. But there is no sensible way of saying "all" initial

> segment. (There is no last line in the Binary Tree.)

Unless there is one missing, we can say all!. And in WM's WMytheology

something is missing.

And in any infinite binary tree complete enough to have every node, it

must also have every sset of nodes, including all those uncountalby many

paths,

>

> The same holds for lists of natural numbers and rational numbers.

> Therefore there is no difference concerning "countability".

>

> Thank you for this discussion it has also helped me to clear thoughts.

Curious then that you have not included any of them here.

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