In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 16 Mrz., 15:47, fom <fomJ...@nyms.net> wrote: > > > Yes, you are focused on the axiom > > of choice. > > Well that's why I raised this topic. And here are my corresponding > questions again: > > 1) Do you agree that Zermelo used a set T consisting of disjoint sets?
WM is indulging in his quantifier dyslexia games again. Zermelo may have done so often. The issue is whether Zermelo did so ALWAYS, and there is sufficient evidence to conclude that he did NOT.
> 2) Do you agree that choosing a number from a set with more than 1 > element means writing or speaking or at least thinking the name of the > number?
NO! Given a nonempty set of naturals, or any other well-ordered set, one can choose a member of that set without writing or speaking or even thinking the name of that member.
> 3) Only finite names can be written, said or thought.
The finite name of an infinite name can be written, said or thought.
> 4) There are only countably many finite names that can be written, > said or thought.
So even in WM's world there can be countably many things?
> 5) Zermelo's AC requires that uncountably many names can be written, > said or thought.
Does this imply that someone else's AC does not?
> 6) In this respect it resembles the statement that a second prime > number triple beyond (3, 5, 7) can be found, perhaps even infinitely > many.
I fail to see any resemblance. Perhaps one must be permanently imprisoned in Wolkenmuekenheim to be able to see it.
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. --