Date: Mar 14, 2013 3:39 AM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Mar 13, 11:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 13 Mrz., 22:41, William Hughes <wpihug...@gmail.com> wrote:
>

> > Let J be a set of the lines of L with no
> > findable last line.  At least two lines
> > belong to J.  Are any lines of J necessary?

>
> Remove all lines.
> Can any numbers remain in the list? No.
> Therefore at least one line must remain in the list.
>
> We do not know which it is, but it is more than no line.
> In other words, it is necessary, that one line remains.


However, it is not necessary that any one particular
line remain. So while it is necessary that the set
J contain one line, there is no particular line l that is
necessary.

<snip>

> From the construction we know, that all numbers, that are in two
> lines, are in one line.


True. And indeed all numbers are in two lines. However,
not the same two lines.

> Therefore your claim, that more than two lines
> must remain in the list, is contradicted.


False. This would only follow if all numbers were in
the same two lines.