In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 11 Apr., 16:42, William Hughes <wpihug...@gmail.com> wrote: > > On Apr 11, 4:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > That is not in question. > > > My claim is this: > > > If we have the propositions (with d_n a digit) > > > A = for every n: P(d_n) > > > B = for every n: P(d_1, d_2, ..., d_n) > > > Then B implies A. > > > > > Do you agree?
Consider the statements A meaning "For every n, d_n is the first n digits of d" and B meaning "For every n, d_1, d_2, ...,d_n are the first n digits of d" Then WM's claim is wrong! > > > > Indeed, however, B does not imply > > > > P(d_1,d_2,d_3....) > > That is not required. It is only required that B implies > A = for every n: P(d_n).
And that claim is wrong. See above. > > > > > So there is no contradiction is saying that A and B > > are true but it it not true that P(d_1,d_2,d_3,...)- > > So A does not imply P(d_1,d_2,d_3,...) either? > > Here is a better presentation: > > In a Cantor list the argument can be written: > For every n: (d_1, ..., d_n) differs from every entry (qk1, ..., qkn) > with k =< n, i.e., i.e., every entry of the first n lines. That is > exactly Cantor's argument, not more and not less.
That is WM's argument. Cantor's was much simpler: Given an infinite list of binary sequences, there is a binary sequnce that differs from the nth sequence in that list at its nth term. > > In a list containing all rational numbers
Cantor's original argument is about binary sequences, and until WM can falsify that one, he fails to falsify its conclusion that there are more binary sequences than can be put into a single sequence of sequnces. --