```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.--
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