In article <firstname.lastname@example.org>, WM <email@example.com> 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.
It appears that WM does misaunderstand, since WH did not mention , or even imply that any line NUMBERS be changed.
> > > Consider the case is potential infinity.
Whyever should we consider what is counter to our reality? You are free to wallow in your own version of reality, but have not the power to impose it on ayone else.
> > But I would ask you in advance: Do you agree that every non-empty set > of natural numbers (including line-numbers) has a smallest element? Or > do you believe that here the exception proves the rule?
That is standard, but what is not is your claim that an inductive set must contain a largest, though unfindable/inaccessible, member. e How are your unfindable naturals any different than inaccessible reals?
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. --