Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 264 Hilbert's Hotel: checking out.
Posted:
May 12, 2013 5:09 PM


In article <2952d61baf7941f49fad087709f2fcef@k5g2000vbq.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 12 Mai, 21:59, Virgil <vir...@ligriv.com> wrote: > > > > > What deludes WM into supposing that either this, or any other method, > > > > will ever have ennumerated ALL irrationals? > > > > > The algebraic irrationals should all be enumerated. None should have > > > escaped. > > > > There are at least as many nonalgebraic irrationals as alegbraic ones > > which counting only the algebraic ones will miss. > > They are not of interest for the current process.
They are for anyone who tries to claim that they are all part of some countable set. > > > > > > Then you have proved in ZFC that there are no rational > > > > > numbers. > > > > > > Not outside of Wolkenmuekenheim. because only the corruptions in > > > > WMytheology allow him to presume any ennumeration of all irrationals. > > > > > I did not say so. Your argument aims at a strawman. > > > > Well you at least implied that being able to count the rationals, even > > though you also have frequenty denied that any such counting is possible > > within Wolkenmuekenheim, also implies countability of the irrationals. > > Contability of the rationals implies countability of the algebraic > irrationals. Nothing else has been required.
The countability of the set of all algebraic numbers, rational or not, was established by Cantor himself, which automatically makes every subset of that set also countable.
And that leaves the rest of the reals the nonalgebraic irrationals, unaccounted for and still uncountable. > > Regards, WM 

