Date: Feb 24, 2013 5:26 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots
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.

>

>

> > f(string) = path

>

> > > > This shows a contradiction

> > > > - at least in case someone accepts

> > > > Hessenberg's trick as part of mathematics.

>

> > > To which Hessenberg, Karl or Gerard or some other one, does WM refer?

>

> > That one who "proved" the uncountability of P(|N), Gerhard that is.

>

> > > And to what alleged "tricks"?

>

> > To look for a set that cannot exist.

>

> What prevents it from existing?

Simplest logic. Try to find a set that contains its number if it does

not contain its number. Isn't that simple?

Regards, WM