Date: Mar 20, 2013 4:40 PM
Author: William Hughes
Subject: Re: Matheology § 224

On Mar 20, 9:31 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 20 Mrz., 21:21, William Hughes <wpihug...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On Mar 20, 9:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > On 20 Mrz., 21:01, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > On Mar 20, 8:57 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > On 20 Mrz., 20:40, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > On Mar 20, 4:24 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > > > I show that every line, that is not the last line, is not needed.
>
> > > > > > Nope.  You show that it is not necessary for its contents.
> > > > > > This is not the same as not needed.

>
> > > > > Agreed:
> > > > > I show that every line, that is not the last line, is not needed to
> > > > > remain in the list in order to have its contents in the list.
> > > > > Agreed?

>
> > > > Nope.  It may be needed for something else whose contents are
> > > > needed (in this case the tail of the list) to exist.

>
> > > Please name a line that is needed for the tail of the list to exist.
> > > (You do agree that every set of lines has a first element?)

>
> > We need an infinite number of lines.
> > Choose lines 3,4,6,7,8...
> > Then line 3, being one of the needed set chosen is needed.
> > Note, that we do not have to choose line 3, so line
> > 3 is not necessary.

>
> Then choose a line that is necessary.


As I have said before, there is no line that is necessary.
This does not mean a set that needs to contain an
infinite number of lines does not contain a line.

> If you say you need an infiinite set of lines, then there must be a
> first one that is needed.


Indeed, but we do not know its identity until after we
have chosen an infinite number of lines.


> Remember: A line is needed if its absence
> changes the set of numbers of the list.


Nope, this is the definition of a line being
necessary. A line is needed if it is one
of the needed number of lines that was
chosen.

A set of needed lines exists.

A set of necessary lines does not.