In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 14 Mrz., 22:28, fom <fomJ...@nyms.net> wrote: > > On 3/14/2013 2:58 PM, Virgil wrote: > > > > > In article > > > > > If that is what Zermelo said then he was wrong to say it because one > > > does not ever "union" elements, only sets. > > > > I want to say that is technically incorrect. > > Of course it is not. He defined, the elements of the set T are > disjoint sets. > > > > Surprisingly, the original 1908 paper introduced > > a union that simply takes a union across the > > elements of the set. > > You do not understand. The elements that Zemelo speaks of are sets. I > give you an example: For instance all subsets of |N are elements of P(| > N).
But outside of certain set theories like ZF, not all elements of a set need be sets. One might have, for instance, the set of people posting to this thread before a certain time. People are not nirmaly considered to be sets so the union of such a set some of whose members are nonsets is a non-set and nonsense.
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. --