In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 16 Mrz., 12:26, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 16, 10:30 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 15 Mrz., 23:27, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Mar 15, 8:34 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > Let's first prove that already two cannot be necessary by the fact > > > > > that two always can be replaced by one of them without changing the > > > > > contents. > > > > > > This is true but the fact that the two lines are > > > > necessary has nothing to do with their contents. Two lines > > > > cannot be replaced by one of them without changing the number > > > > of lines. > > > > > Why should line-numbers be changed? Perhaps we are misunderstanding > > > each other. > > > > I said "number of lines" not "line-numbers". > > If you replace two lines by one of them, you do > > not change the contents, but you do change the number > > of lines. Since the number of lines is important > > and the contents are not, you cannot replace > > two lines with one line. > > Ok, I understand. Anyhow, if the number of lines is not empty, then > there must remain at least one line as a necessary line. That line has > a line-number in the original list. I think that if one more more > lines are necessary, as you claim, then there must be a set of line- > numbers which is not empty and, therefore, has a least element.
On the other hand, such a set of lines cannot have a largest element, at least outside of Wolkenmuekenheim, since, at least outside of Wolkenmuekenheim, for every line is a proper subset of infinitely many successor lines. > > Do you think that this is unmathematical?
What goes on in Wolkenmuekenheim certainly is, alt least by the standards of real mathematics.
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. --