Date: Mar 20, 2013 4:07 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 20 Mrz., 20:02, Virgil <vir...@ligriv.com> wrote:
> In article
> <52fc6409-ea7d-4704-9782-6ba192770...@z3g2000vbg.googlegroups.com>,
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 20 Mrz., 14:00, William Hughes <wpihug...@gmail.com> wrote:
> > > On Mar 20, 1:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > <snip>
>
> > > > > So your proof that any two lines can be replaced
> > > > > by one line without changing the contents is irrelevant.

>
> > > > Since contents can only exist in lines, and since every line is
> > > > superset to all its predecessors, the proof is correct.

>
> > > The proof is irrelevant (it is, however, correct)
>
> > Nice to hear. Not that I had any doubt, but it is nice to hear that
> > you have no doubt too.

>
> > > since showing that lines are not needed for their
> > > contents does not show that the lines are not needed.

>
> > The lines were invented by myself solely for this purpose.
>
> Then the invention was futile for your purpose was not achieved, as at
> least infinitely many of those lines are necessary and have been proved
> to be.


Does every infinite set contain at least two elements?
Does every two-element-set of enumerated elements contain a first
element?

If you agree, name the first element of your infinite set. If you
don't agree, please disappear out of sci.logic.
>
>
>

> > The first question is:
> > Is the first line necessary to have the number 1 in the list.

>
> > Formulated somewhat more "mathematically":
> > Is the union of all lines different from the union of all lines except
> > the first one.

>
> Theorem: Every finite union of lines omits some naturals and every
> infinite union of lines includes all naturals


and probably also all quaternions and all race-horses, because
infinity is very powerful. It destroys ever sober thought and every
reasonable idea.

Regards, WM