```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 afirst one that is needed. Remember: A line is needed if its absencechanges the set of numbers of the list. You state that a set of linesall 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-enumeratedset. Compare my original example with the table-top.Regards, WM
```