In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 15 Mrz., 13:56, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 14, 10:31 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 14 Mrz., 08:39, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Mar 13, 11:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 13 Mrz., 22:41, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > Let J be a set of the lines of L with no > > > > > > findable last line. At least two lines > > > > > > belong to J. Are any lines of J necessary? > > > > > > > Remove all lines. > > > > > Can any numbers remain in the list? No. > > > > > Therefore at least one line must remain in the list. > > > > > > > We do not know which it is, but it is more than no line. > > > > > In other words, it is necessary, that one line remains. > > > > > > However, it is not necessary that any one particular > > > > line remain. So while it is necessary that the set > > > > J contain one line, there is no particular line l that is > > > > necessary. > > > > > Correct. But I have not claimed that there are particular lines. > > > > Then it is a mistake to call particular line necessary > > e.g. to say "There is a necessary line".- > > I don't say that there is a necessary line. It is necessary, that > there remains a line or two. In detail: > > In potential infinity it is necessary that at least one line has to > remain undeleted in order to contain all natural numbers that are in > the list.
In potential infinity, there is always a last line, therefore a maximal, last natural having no successor.
Which makes its last member a very unnatural natural. > > In actual infinity it is necessary that at least two lines have to > remain undeleted in order to contain all natural numbers of |N.
It is naturally necessary that there be more than one line and also that for each line there must also be a subsequent line, to get all naturals of |N. > > No special line is necessary. But we know that two or more lines can > never do a better job than one. So whatever lines may remain, the > assertion is falsified.
But any set of infinitely many lines do a better job than any finite set of lines, since for any finite set of lines there is a successor line longer than any of them. > > I have explained this in WMytheology § 224.
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. --