In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 11 Apr., 23:52, William Hughes <wpihug...@gmail.com> wrote: > > On Apr 11, 9:51 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 11 Apr., 20:52, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Apr 11, 8:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 11 Apr., 19:19, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > So you agree that B implies A. > > > > > > > > yep, but A does not imply C: P(d_1,d_2,d_3..) > > > > > > > That is your interpretation. > > > > > > One you agree with, > > > > > Not at all! > > > > Yep, you have agreed that saying something is true for > > every element of a collection does not imply that it > > is true for the collection. > > It is true for all elements. No mentioning of collection. I am not at > all interested whether these elements form something like a > collection. Of course you cannot say that the collection of real > numbers is a real number. But when all real numbers have been removed, > the collection has gone too.
So there must have been a set of all real numbers to eliminate.
> > Then Cantor's argument fails from the scratch. Cantor uses the fact > that removing every line from the set L of possible duplicates of the > anti-diagonal d does not leave any line.
Cantor does not need to use anything of the sort.
Cantor merely uses the fact that if two infinite binary sequences differ in at least one position then they are different sequences, and shows how to build such a sequence different from every such sequence in any given list of such sequences.
WM keeps claiming that the Cantor argument says things that it does not say. --