In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 13 Mrz., 13:19, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 13, 11:38 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 12 Mrz., 17:09, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Mar 12, 5:00 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 12 Mrz., 16:50, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > I say a lot of wrong things. But it > > > > > > does not matter much. Anything I > > > > > > say can easily be translated into > > > > > > something correct. > > > > > > > How would you translate your credo: The list contains more numbers > > > > > than fit into a single line? This sentence is completely foreign to > > > > > potential infinity. > > > > > > Let the potentially infinite sequence of > > > > numbers in the list be X. > > > > There is no findable line that is coFIS to (X). > > > > > And perhaps you will show some such numbers, at least two, which do > > > not fit into one single line? > > > > There are no such numbers (in either actual or potential > > infinity) and I have never claimed that there are. > > The claim that all numbers are there and not all are in a single line > implies that all numbers are in at least two different lines. That > logic cannot be circumvented.
That "logic" assumes a condition contrary to fact, that in an endless sequence of lines there is a last line.
Since each line has a successor line longer than all its predecessor lines, and each has a larger natural that any of it predecessors, only a non-existing "last line" could contain all naturals, but there is no last line. > > > If you wish to contest this, use my words not > > yours (e.g. I have never said "The list contains more > > numbers than fit into a single line", I have said > > "There is no line in the list which contains every > > number in the list".) > > Correct. The list has more numbers than a single line has. Since every > number that is in the list, must be in at least one line, this implies > that the numbers are in more than one line. More than one, in > quantized systems like lists, meams two at least.
It is equally provable to require more than two line, or, indeed, more than any natural number of lines.
Thus no finite set of WM's lines is sufficient to contain all WM's naturals. Or anyone else's naturals, either.
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. --