Date: Mar 20, 2013 10:41 PM Author: Virgil Subject: Re: Matheology � 224 In article

<04deaa36-9b5c-4fa5-852e-f191306f0cab@ia3g2000vbb.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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 necessary

>

> in order to have all naturals in the list.

>

> > This does not mean a set that needs to contain an

> > infinite number

>

> If the set needs to contain an infinite number of lines, then this is

> a 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 no

> necessary 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 chosed

> set of lines we can prove that the lines are completely superfluous

> for 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.

Nope!

Any sufficient set of lines will have a first element, but as there are

pairs of such sufficient sets which are disjoint, there is no first

element common to all sufficient sets.

> If lines were chosen, that are superfluous, they cannot belong to the

> needed number.

The number of lines needed is infinite, but there are infinitely many

pairwise disjoint sets of lines which each of which is sufficient.

> >

> > A set of needed lines exists.

>

> Name the frist line. Or confess that not every set of natural numbers

> is a set if natural numbers that obeys the rules established in set

> theory for sets of natural numbers.

That first sentence is not English.

That second sentence does not scan in ENglish eoither..

> >

> > A set of necessary lines does not.-

>

> Ah, a needed line is not a necessary line?

No particular line is needed as long as some subsequent line is included.

All that is required is a non-empty set of lines with no last line.

Since in WMytheology this seems to be impossible, WM's mathematics is

necessarily incomplete.

>

> In order to avoid interpretations of need an necessity, simply adhere

> to this definition: A line is HIGH, if it cannot be removed without

> changing the contents of the list, i.e., |N.

>

> Theorem, valid in actual infinity: No line is necnee. There is no set

> of necnee lines.

The conditions of necessity or sufficiency on sets of lines needed to

contain all naturals do not involve particular lines, but only involve

the sizes of the sets.

That WM refuses to acknowledge this is just another measure f his almost

universal incompetence as a mathematician.

WM cannot even sort out linearity properly!

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