```Date: Mar 20, 2013 5:01 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 20 Mrz., 21:40, William Hughes <wpihug...@gmail.com> wrote:> 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 necessaryin order to have all naturals in the list.> This does not mean a set that needs to contain an> infinite numberIf the set needs to contain an infinite number of lines, then this isa set that has to have a first element.> of lines does not contain a line.It cannot contain a necessary line, since, as you said, there is nonecessary line.But you think that it necessarily must contain a not necessary line.If so, then at least one line is necessary. If so then the set of non-necessary lines which are necessary contains a first line.Name it!>> > 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.Even afterwards we do not know its identity, because of every chosedset of lines we can prove that the lines are completely superfluousfor the contents of the list.>> > 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 needed number of lines has a first element.If lines were chosen, that are superfluous, they cannot belong to theneeded number.>> A set of needed lines exists.Name the frist line. Or confess that not every set of natural numbersis a set if natural numbers that obeys the rules established in settheory for sets of natural numbers.>> A set of necessary lines does not.-Ah, a needed line is not a necessary line?In order to avoid interpretations of need an necessity, simply adhereto this definition: A line is HIGH, if it cannot be removed withoutchanging the contents of the list, i.e., |N.Theorem, valid in actual infinity: No line is necnee. There is no setof necnee lines.Regards, WM
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