In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 20 Mrz., 21:01, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 20, 8:57 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 20 Mrz., 20:40, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Mar 20, 4:24 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > I show that every line, that is not the last line, is not needed. > > > > > > Nope. You show that it is not necessary for its contents. > > > > This is not the same as not needed. > > > > > Agreed: > > > I show that every line, that is not the last line, is not needed to > > > remain in the list in order to have its contents in the list. > > > Agreed? > > > > Nope. It may be needed for something else whose contents are > > needed (in this case the tail of the list) to exist. > > Please name a line that is needed for the tail of the list to exist.
Since there are may pairwise disjoint pairs of sets of FISIONs which suffice, no particular line, or even finite set of lines in necessary. What is both necessary and sufficient for a set of lines/FIDONs to contains all natuarls is that that set be infinite.
> (You do agree that every set of lines has a first element?)
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. --