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


Re: Matheology � 223: AC and AMS
Posted:
Mar 15, 2013 7:09 PM


In article <ca1c15ef51b44499b79f42944951150e@j9g2000vbz.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 15 Mrz., 21:01, Virgil <vir...@ligriv.com> wrote: > > In article > > <c4fcdc6876bb4df0a2f573d117d0b...@m4g2000vbo.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fhaugsburg.de> wrote: > > > On 14 Mrz., 23:54, fom <fomJ...@nyms.net> wrote: > > > > On 3/14/2013 5:47 PM, WM wrote: > > > > > > > On 14 Mrz., 23:16, fom <fomJ...@nyms.net> wrote: > > > > > > >> "... an element of T is not a set..." > > > > > > > Let T = {{a}, {b,c}, {c,d,e,f}} > > > > > then T has three elements, each of which is a set. That is common use > > > > > in modern set theory and has been used 100 years ago in the same sense > > > > > by Zermelo. > > > > > > I am well aware of modern usage. > > > > > Zermelo used it already 100 years ago. > > > > > > 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, even if accurate, in no way refutes that Zermelo allowed sets to > > contain urelements. > > That is not under discussion and therefore not refuted.
It IS under discussion above, but even if it were not, the refutation is valid.
> > fom said: an element of T is not a set > Zermelo said: T is a set whose elements M, N, R,
Which in no way implies that only sets can be elements.
According to WM's line of reasoning, if some set contains only natural numbers, all sets are automatically prohibited from containing anything else. > > Simple as that. (Of course, I know, that in matheology everything is > quite different. You need not explicate that in detail.)
Everyone is by now aware that outside your miniscule world of WMytheology, in what you label matheology but is actually majority mathematics, one can achieve a lot of things, in fact far more that an a moiety of modern mathematics, that is banned in your WMytheology.
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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. 

