In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 15 Feb., 23:58, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 15, 10:30 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 15 Feb., 00:44, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > Two potentially infinite sequences x and y are > > > > > > equal iff for every natural number n, the > > > > > > nth FIS of x is equal to the nth FIS of y > > > > > > So we note that it makes perfect sense to ask > > > > if potentially infinite sequences x and y are equal, > > > > > and to answer that they can be equal if they are actually infinite. > > > But this answer does not make sense. > > > You cannot prove equality without having an end, a q.e.d.. > > > > A very strange statement. Anyway there is no reason to > > claim equality. Let us define the term coFIS > > > > Two potentially infinite sequences x and y are said to be > > coFIS iff for every natural number n, the > > nth FIS of x is equal to the nth FIS of y. > > > > So for every natural number the list > 1 > 12 > 123 > ... > is coFIS with its diagonal.
WRONG! for your list, L FIS1(L) = 1, FIS2(L) = 1, 12, FIS3(L) = 1, 12, 123 and so on whereas for the diagonal, D = 123... FIS1(D) = 1 FIS2(D) = 12 FIS3(D) = 123 and so on
So the list of FISs of an endless list like D can never be the same as the the list itself.
But note for an antidiagonal to L, like A = 234... FIS1(A) = 2, FIS2(A) = 23 FIS3(A) = 234 and so on > > > We note that it makes perfect sense to ask > > if potentially infinite sequences x and y are coFIS, > > up to every n. Correct. And that is the case in the list.
But no list is coFIS with the list of its FISs. > > > we have cases where they are not coFIS and cases > > where they are coFIS.. We also note that no > > concept of completed is needed, so coFIS can > > be demonstrated by induction. In particular, you > > do not need a last element to prove that x and y > > are coFIS. > > > > So WMs statements are > > > > there is a line l such that d and l > > are coFIS > > Of course, for every n there is a line 1, 2, 3, ..., n that is coFIS > to the diagonal 1, 2, 3, ..., n. And there is not more than every n.
WRONG! SEE ABOVE!
No list is ever coFIS with the list of its FISs.
> > > > > there is no line l such that d and l > > are coFIS > > That would only be true if there was an n larger than every n, either > in a line or in the diagonal.
WRONG! WM's list l is a list of lists whereas the d is a list of digits They can never be coFIS.
> But that would not only require actual > infinity but also the diagonal surpassing every line or some line > surpassing the diagonal. Both is impossible by construction.
What is claimed to be impossible by WM in his Wolkenmuekenheim is often trivial elsewhere, and what is impossible elsewhere WM often claims is trivial in his Wolkenmuekenheim.
So the wise are not deluded by what goes on in Wolkenmuekenheim. > > Do you know an n of the diagonal that is not in a line? Or vice versa? The only FIS of WMs list of lists, l, which is at all like a FIS of d is the very first one, after which they are all entirely different. --