Date: Feb 24, 2013 4:51 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<db72e90a-02f6-4a81-8193-e84e6e2ef553@k4g2000yqn.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Feb., 01:19, Virgil <vir...@ligriv.com> wrote:
>

> > > >  There is certainly no meaning of "linear" in English
> > > > mathematics that is appropriate.

> >
> > > Then use German mathematics. There it is.
> >
> > > f(ax + by) = af(x) + bf(y)
> >
> > With suitable interpretations for f, a, b, x and y, this would makes f a
> > linear function.

>
> It is not hard to find this interpretation in mathematics.

> >
> > But if f is to be a mapping between the set of all paths of a Complete
> > Infinite Binary Tree and the set of all subsets of |N, which is the only
> > sort of mapping under consideration when WM claimed linearity, I defy WM
> > to come up with an appropriate definition of a,b,x and y which will make
> > such an f a linear mapping.
> >

>
> Two binary strings are treated like two real numbers. In fact they are
> nothing but representations of real numbers.


That in no way makes any mapping between the set of all such binary
strings and the set of all paths of a CIBT into a LINEAR mapping.

At least until WM has formulated both that set of binary sequences and
that COMPLETE INFINITE BINARY TREE as a linear spaces over some field ,
and then shown that his mapping is a linear mapping between those linear
spaces. None of which he has done.



>
> Simplest logic. Try to find a set that contains its number if it does
> not contain its number. Isn't that simple?




How does that apply to, say, the set of von Neumann natural numbers in
ZF?

In the von Neumann model a natural does not ever contains its number,
only the numbers of previous naturals.

So in that von Neumann model, WM's above objection fails.
--