Date: Feb 25, 2013 9:08 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
WM <> wrote:

> On 25 Feb., 13:46, William Hughes <> wrote:
> > On Feb 25, 1:09 pm, WM <> wrote:
> >

> > > On 25 Feb., 12:20, William Hughes <> 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.

In a world more sane than WMytheology, if every line is not a last line,
there is no last line.
> Your assertion can be proven wrong for *every* line. But you believe
> that it is right for infinitely many? Mathematics looks different!

What is wrong for individuals can be right for a set of those
> >
> > 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.

Find us one that contains all that its successors do.
> > 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.

If, as in your examples, each line, l, is a FIS of d, but not all of d,
then no one line can contain what the next line contains, and every next
line is necessary to get all 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.

And that is all irrelevant to the fact that you cannot have it all when
you insist on stopping before getting it all.

WM's world does not allow induction as a method of proof, because it
always requires stopping after a finite number of steps.