In article <aa348889-9e3b-4299-b906-e1d53ac96f85@s12g2000yqi.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 30 Mai, 00:18, Virgil <virg...@nowhere.com> wrote: > > > > It is wrong for complete sets. > > > > By which WM means finite ones, but no one has claimed otherwise. > > Complete means finished = finite. > > Cantor, in his diagonal proof of the incompleteness of any list of > > binary sequences, does NOT assume that the given list is complete. > > > > He merely proves that any given list is incomplete. > > > > The Cantor challenge is: Provide me with a list of infinite binary > > sequences and I will show you how to find one not in that list. > > That is not difficult to satisfy : The complete list of all real > numbers starts just at that position n+1 where you will cease to seek > it.
Perhaps WM will cease to seek it at some finite natural, but mathematicians are not so easily discouraged, and will persist beyond the successor of any such finite natural.
And according to the terms of the Cantor challenge in that proof, it is up to those who challenger Cantor to provide the list of seequnces, and Cantor only needs show there is a sequence not in that list. Which Cantor succeeds in showing can always be done.
It is a shame that WM never seems able to comprehend what the Cantor "diagonal" proof actually says.
