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