In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 17 Mrz., 19:49, Virgil <vir...@ligriv.com> wrote: > > > > Zermelo created the axiom of choice because it was obvious to him that > > > is is correct, i.e., that his choice can be done, at least in > > > principle. Then he went on and "proved" from this axiom the well- > > > ordering theorem. If he had known that the axiom of choice can be > > > disproved by proving that at most countably many choiced can be > > > executed, even in principle, why should he have used it? > > > > Standard mathematics does not accept any such claimed disproof as valid! > >
WM has frequently claimed that HIS mapping from the set of all infinite binary sequences to the set of paths of a CIBT is a linear mapping.
In order to show that such a mapping is a linear mapping, WM would first have to show that the set of all binary sequences is a linear space (which he has not done and apparently cannot do) and that the set of paths of a CIBT is also a vector space (which he also has not done and apparently cannot do) and then show that his mapping, say f, satisfies the linearity requirement that f(ax + by) = af(x) + bf(y), where a and b are arbitrary members of the field of scalars and x and y and f(x) and f(y) are arbitrary members of suitable linear spaces.
While this is possible, and fairly trivial for a competent mathematician to do, WM has not yet been able to do it.