Date: Mar 20, 2013 2:44 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<a5cde608-ccdf-41f7-abe4-a870495d193e@14g2000vbr.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 19 Mrz., 09:53, William Hughes <wpihug...@gmail.com> wrote:
> > On Mar 19, 8:49 am, WM <mueck...@rz.fh-augsburg.de> wrote:> On 19 Mrz.,
> > 00:44, William Hughes <wpihug...@gmail.com> wrote:
> >
> > Do you agree with the statement.
> >
> > If a set of lines contains an unfindable line then
> > it contains two findable lines.

>
> No.

> >
> > ?
> >
> >
> >

> > > > > But the more pressing question is: You construct a list such that
> > > > > every line contains all preceding contents. You get ready, i.e., the
> > > > > list contains all that it can contain. Nevertheless there is no line
> > > > > that contains everything that the list contains.

> >
> > > > Yep, no last line.
> >
> > > Do you recognize that this is no explanation for your assertion that
> > > in our list more than one line contain more than one  line contains?

> >
> > Nope.  Clearly only the last line contains everything
> > in the list.  If there is no last line, then no line contains
> > everything in the list.

>
> This leaves two escapes:
> Either there is a list that contains everyting that the list contins
> in two or more lines.


Since each line has a successor line and is a proper subset of that
successor line, the only "escape" is to have a nonempty set of lines
with no last line.

> Or, it is unreasonable to talk about everything that the list
> contains.

> >
> > Note that lines are needed for other reasons than just their
> > contents.

>
> The meaning of your words is dark. Nevertheless:
> Lines are required for their contents to be in the list.
>

> > So your proof that any two lines can be replaced
> > by one line without changing the contents is irrelevant.

>
> Since contents can only exist in lines, and since every line is
> superset to all its predecessors, the proof is correct. It shows that
> actual infinity is unreasonable.


It does not show any such thing when not in Wolkenmuekenheim.

And WM's alleged "bijective linear mapping" from the set of all binary
sequences via the reals onto the set of all paths of a Complete Infinite
Binary Tree is still not actually a linear mapping, and cannot be onto
as described.

But there is a bijective linear mapping from the set of all binary
sequences onto the set of all paths of a Complete Infinite Binary Tree
that WM has not been able to find.
--