In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 10 Apr., 13:40, Dan <dan.ms.ch...@gmail.com> wrote: > > On Apr 10, 1:33 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 10 Apr., 08:59, William Hughes <wpihug...@gmail.com> wrote: > > > > > > Next argument.- > > > > > Consider a Cantor-list that contains a complete sequence (q_k) of all > > > rational numbers q_k. The first n digits of the anti-diagonal d are > > > d_1, d_2, d_3, ..., d_n. It can be shown for every n that the Cantor- > > > list beyond line n contains infinitely many rational numbers q_k that > > > have the same sequence of first n digits as the anti-diagonal d. > > > Proof: There are infinitely many rationals q_k with this property. > > > All are in the list by definition. At most n of them are in the first > > > n lines of the list. Infinitely many must exist in the remaining part > > > of the list. So we have obtained: > > > For all n exists k: d_1, d_2, d_3, ..., d_n = q_k1, q_k2, q_k3, ..., > > > q_kn > > > > > Every property that holds for all FISs d_1, d_2, d_3, ..., d_n of d, > > > also holds for all digits d_n of d that can be subject to digit- > > > reversal and digit comparison. > > > > > > They have the same sequence of first n digits, but you'll never find a > > number in the list that has "all digits the same as the anti- > > diagonal" . > > For all n is not for all n? d has more digits than all? > My proof is valid for all n.
Your argument only holds for finite sequences, but any anti-diagonal, by not being a finite sequence, is exempt.
If you can name a digit d_n that is not > covered, please let me know. If not, then you should think over your > basis of doing mathematics. > > > > For any natural number k , the k'th member of your list will have its > > k'th digit different from the k'th digit of the antidiagonal . > > Therefore the antidiagonal itself is not in the list , even as > > arbitrarily large "partial sub-sequences" of the antidiagonal may > > appear on the list .- Ziti > > Your conclusion is wrong.
Not anywhere nearly as wrong as your arguments.
WM's argument is essentially that what is true for finite sequences must be true for infinite sequences as well. WHich can only be true in some corrupt system like WMytheology, which only holds in the crypts of Wolkenmuekenheim. --