In article <b1d23660-1b7a-4682-affa-952cf2d9e03b@e34g2000pra.googlegroups.com>, Newberry <newberryxy@gmail.com> wrote:
> On Jun 20, 1:18 pm, 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". > > > > What that proof (not actually by by Cantor himself) ays is that any > > listing of reals is necessarily incomplete because given such a listing > > one can always construct a real not listed in it. > > Please CONSTRUCT the anti-diagonal in the space provided below. > > Virgil's anti-diagonal construction > BEGIN
It is not mine but Cantor's, though the following notation is mine.
N represents the set of natural numbers.
NxN is the Cartesian product of N with itself with members (m,n) where m and n are members of N.
F: NxN --> {0,1} is a list of functions, F(m,--), from N to {0,1} with, for each m in N, F(m,--): n --> F(m,n), being such a function.
Then the anti-diagonal function g:N --> {0,1} is defined by g(n) = 1-F(n,n) in {0,1}, so that g(n) <> F(n,n) for all n, and thus g(--) <> F(n,--) for all n..
Note the Cantor himself never published an anti-diagonal argument for the reals themselves, though some of his followers did.
> > > > END > > > What Cantor himself proved was that for any list of infinite binary > > sequences there are binary sequences not listed in that list. > > > > Cantor had previously proved by quite a different method, which WM seems > > unable or unwilling to criticize, that the set of reals was not > > countable. > > > > > > > > > Even completely blinded matheologicians should be able, perhaps after > > > some contemplation, to recognize that. > > > > What completely blinded matheologicians are able, perhaps after > > some contemplation,to recognize is that WM is not working in the same > > world as mathematicians do.
