Virgil
Posts:
9,012
Registered:
1/6/11


Re: Matheology � 223: AC and AMS
Posted:
Mar 15, 2013 7:17 PM


In article <1adc7c3b0a824108bd605e5e6ee12ac3@y9g2000vbb.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> 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 urelements in sets other than in ZFC.
SO that WM is again shown to be in the wrong!
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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.
> > Regards, WM 

