Date: Mar 21, 2013 1:17 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
WM <> wrote:

> On 21 Mrz., 08:57, William Hughes <> wrote:
> > On Mar 21, 8:46 am, WM <> wrote:
> >

> > > My question remains: What is the subset of necessary lines?
> >
> > There is no such thing as a necessary line.

> Correct. That is because the asserted aim cannot be established.

How is it that in WMytheology the set of all lines does not contain
somewhere every member of every line?

> > There is such a thing as a sufficient set of
> > lines  (all sufficient sets are composed
> > entirely of unnecessary lines, which means
> > that you can remove any finite set of lines

> Why only finite sets?

He did not say only finite sets of lines. And it possible from any
infinite set of lines to remove all but infinitely many, which does
allow removal of infinitely many.

> If there are infinitely many unnecessary lines, they all can be
> removed -

Only in Wolkenmuekenheim.

> You try to cheat

WM actually does cheat, but does it so badly, he almost alwasys gets
caught at it.
> > from a sufficient set and get a different sufficient
> > set of lines).

> You claim that there is a sufficient set

The set of all lines is obviously sufficient to cover all naturals, but
is equally obviously not necessary, as any one line can be removed
without uncovering any natural.

In fact, from any set of lines that is sufficient, any one line can be
removed and the set of remaining lines will still be sufficient, but if
one removes infinitely many lines what remains need not be sufficient.

> but every line you have
> offer ed up to now is not necessary and not sufficient. Amazing that
> you want to sell that as mathematics.

It is quite good asmathematics, it is only bad as WMytheology.

> Try to answer this question to yourself: Why do you claim that an
> infinite set of unnecessary lines must not be removed completely

I don't claim that.

Outside of Wolkenmuekenheim, from any set of lines sufficient to cover
all naturals SOME, but not all, infinite sets of lines may be removed
and still leave all naturals covered.



WM claims to know how to map bijectively the set of infinite binary
sequences, B, linearly to the set of reals and then map that image set
of reals linearly ONTO the set of all paths, P, of a Complete Infinite
Binary Tree.

But each binary rational in |R is necessarily the image of two sequences
in B but that one rational can then only produce one image in P, so the
mapping cannot be the bijection WM claims.

SO that WM is, as usual with things mathematical, wrong.