In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 15 Mrz., 20:17, fom <fomJ...@nyms.net> wrote: > > On 3/15/2013 3:20 AM, WM wrote: > > > > > On 14 Mrz., 23:54, fom <fomJ...@nyms.net> wrote: > > > > >> Unless my translation is in error, Zermelo's > > >> 1908 supports urelements. > > > > > Zermelo says (in your translation on p. 210, 3rd line): If T is a set > > > whose elements M, N, R, ... all are sets different from the null > > > set, ... > > > > That is Zermelo's description of the > > axiom of choice. > > T is the domain, the set which Zermelo uses to demonstrate his > intention of the axiom of choice. > > > It is not the description of his domain. > > > > I gave the relevant passages > > Not for ZFC. There everything is a set.
But as Frankel outlived Zermelo, ZF and ZFC need not be pure Frankel, and and Frankel may well have allowed ur-elements in sets other than in ZFC.
WM has frequently claimed that a 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 must first show that the set of all binary sequences is a vector space and that the set of paths of a CIBT is also a vector space, which he has not done and apparently cannot do, and then show that his mapping satisfies the linearity requirement that f(ax + by) = af(x) + bf(y), where a and b are arbitrary members of a field of scalars and x and y are f(x) and f(y) are vectors in suitable linear spaces.
By the way, WM, what are a, b, ax, by and ax+by when x and y are binary sequences?
If a = 1/3 and x is binary sequence, what is ax ? and if f(x) is a path in a CIBT, what is af(x)?
Until these and a few other issues are settled, WM will still have failed to justify his claim of a LINEAR mapping from the set (but not yet proved to be vector space) of binary sequences to the set (but not yet proved to be vector space) of paths ln a CIBT.
Just another of WM's many wild claims of what goes on in his WMytheology that he cannot back up.