Date: Feb 24, 2013 4:51 PM
Subject: Re: Matheology � 222 Back to the roots
WM <firstname.lastname@example.org> 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
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.