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