On Tuesday, December 3, 2013 1:15:26 AM UTC-7, WM wrote: > Am Dienstag, 3. Dezember 2013 03:34:35 UTC+1 schrieb Zeit Geist: > > On Monday, December 2, 2013 1:58:01 PM UTC-7, WM wrote: > > > > Fine, then undefinable numbers cannot result from any Cantor-argument - and other theories do not contain them. So, why the heck do you think undefinable numbers exist? > > > Although quite useful, not all of Set Theory depends on the Diagonal Argument. > > But all mathematics depends on definable numbers and does not allow to construct, or obtain in any other way, undefinable numbers.
Where in the Axiom Set for the Real Numbers are "Defined Numbers" mentioned?
Where in you posts have you given a a Formal Conception of "Definable Numbers"?
> > In fact, the existence or non-existence of non-constructible Real Numbers is Independent from the Axioms of ZFC. > > No. ZFC has uncountability. Definable numbers have not.
Could you give an example of a Model of ZFC in which all Real Numbers are definable and that contains a Bijection between N and R.
> > Some Models contain them, and some don't > > The latter must be countable.
Really? Show me! You seem so convinced of it. You should be able to Prove it.