Date: Mar 13, 2013 12:59 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Mar 13, 5:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 13 Mrz., 13:19, William Hughes <wpihug...@gmail.com> wrote:

<snip>

> > If you wish to contest this, use my words not
> > yours  (e.g.  I have never said "The list contains more
> > numbers than fit into a single line",  I have said
> > "There is no line in the list which contains every
> > number in the list".)

>
> Correct. The list has more numbers than a single line has. Since every
> number that is in the list, must be in at least one line, this implies
> that the numbers are in more than one line.


To be precise, a set of lines, say K, that contains all the numbers
contains at least two lines. However, this does *not* imply that
there are two numbers that are not in a single line.
Nor does it imply that there is a necessary line in K.
Note that a sufficient set does not imply a necessary line
even in potential infinity. There is no line that is needed
to make L have an unfindable last line.