In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 20 Jun., 22:18, Virgil <Vir...@home.esc> wrote: > > In article > > <f92c169d-ee85-40c2-aa82-c8bdf06f7...@j4g2000yqh.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 20 Jun., 17:51, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > > > > > > Cantor was this utterly insane freak who chose not to accept Newberry's > > > > word for it, and instead *prove* that there was no list of all real > > > > numbers. Obviously, his proof is nonsense, because, after all, Newberry > > > > said there was no list. > > > > > His proof is nonsense because it proves that a countable set, namely > > > the set of all reals of a Cantor-list and all diagonal numbers to be > > > constructed from it by a given rule an to be added to this list, > > > cannot be listed, hence, that this indisputably countable set is > > > uncountable. > > > > That is a deliberate misrepresentation of the so called "diagonal proof". > > But this proof can be applied to this countable set and shows its > uncountability.
For every list of binary sequences, that list plus its "anti-diagonal" sequence can be listed. But there is no such list for which the "anti-diagonal" is a member of the list, so none of those lists ennumerates the set of ALL such sequences. Thus the set of all such sequences cannot be listed, or, equivalently, counted.
Mutatis mutandis, the same is true for listing reals.