In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 16 Mrz., 19:26, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 16, 7:10 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 16 Mrz., 18:10, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > Ok, I understand. Anyhow, if the number of lines is not empty, then > > > > > there must remain at least one line as a necessary line. > > > > > > Not a particular line. This is similar to > > > > the case where any set of lines with an unfindable > > > > last line has at least one "necessary" findable line. > > > > This line has a line number in the original > > > > list but we can choose the "necessary" > > > > findable line to have any line number we want. > > > > > No, it is always the last line. We call it unfindable or unfixable > > > because as soon as we have found it, it is no longer the last line. > > > > Note, that I am not talking about the unfindable line, > > but the "necessary" findable line. We can choose this > > line to have any line number we want > > In potential infinity there is no necessary line except the last one. > We know that with certainty from induction. Every found and fixed line > n cannot be necessary, because the next line contains it.
AS soon as something is identifies as a natural or a FIS of the set of naturals, it has a successor. It cannot be either a natural nor a FIS of the naturals without a successor. at least by any standard definition of naturals.
Can WM provide an definition for natural numberss which doe not state, or at least imply, that every natural must have a successor natural?
> > Everything that is in the list > 1 > 1, 2 > 1, 2, 3 > ... > 1, 2, 3, ..., n > is in the last line. Alas as soon as you try to fix it, it is no > longer the last line.
Thus it is unfixable that where there is a last line there are not all lines nor all naturals. > > Think of the time. What is "now"? As soon as you try to fix it, it is > past. In time you can predict the development of clocks. In lists > there is no such smooth, predictable evolution. Will the next line > added to above list be n+1, or n^2 or n^n^n^n (all those of course > also including n+1 and its followers? There are no limits. But as soon > as we look onto the last line, we get the idea of another one and that > will add one or many lines to the list.
So that the process is endless.
Mathematics outside of Wolkenmuekenheim deals successfully with endless processes all the time, but inside Wolkenmuekenheim, they are apparently totally verbotten. >
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. --