Date: Feb 25, 2013 9:53 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 25 Feb., 13:46, William Hughes <wpihug...@gmail.com> wrote:
> On Feb 25, 1:09 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > On 25 Feb., 12:20, William Hughes <wpihug...@gmail.com> wrote:
> > > Only those people who care
> > > about unfindable natural numbers (a group that
> > > includes WM but not me) are interested

>
> > No? The numbers of those lines that contain what, according to your
> > assertion, cannot be contained in one line, are unknowable

>
> [The term is "unfindable"]


Wrong. You can easily define what line is requires, bamely the first
line of your asserted set of infinitely many lines that are necessary
to contain more than one line can contain.

You cannot know that first line, because every line can be proven to
be *not* such a line.

Your assertion can be proven wrong for *every* line. But you believe
that it is right for infinitely many? Mathematics looks different!
>
> Nonsense.  The "numbers of those lines that contain what, according to
> your
> assertion, cannot be contained in one line" is a set of numbers,
> no single number has this property.


I know that every number n has the property that the line l_n contains
all that its predecessors contain. Note, these n are numbers.

> The set is the potentially
> infinite set {1,2,3,...}.  All of these are "findable".  I do not use
> and am not interested in "unfindable" natural numbers.


Once upon a time you have been asserting that more than one line are
necessary to contain all that can be contained of d. This collection
of lines may be a set - it does not matter. But every set of lines of
L has a first element. You cannot name the first element l_n, you
cannot name the n. And that is a number.

So you believe in unnameable numbers.
Note, the number is defind. It is the first one that you maintain to
exist. It is the most important one for your kind of mathematics. And
you need infinitely many such numbers , I need only one such number.
Ain't I to envy?

Regards, WM