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?