Date: Mar 20, 2013 4:31 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

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.
If you say you need an infinite set of lines, then there must be a
first one that is needed. Remember: A line is needed if its absence
changes the set of numbers of the list. You state that a set of lines
all of which are needed does exist.
>
> Compare to choosing a basis for |R^2.  Two vectors
> are needed.  However, there is no necessary vector.-


That is the difference between an enumerated set and a not-enumerated
set. Compare my original example with the table-top.

Regards, WM