In article <firstname.lastname@example.org>, email@example.com wrote:
> On Sunday, 4 May 2014 20:53:17 UTC+2, Zeit Geist wrote: > > > > > I use the well-established theorem of ZF that every infinite subset of a > > > countable set is countable. > > > > > But ignore the Theorem that Not All Subsets of a Definable Countable Set > > are Definable! > > No I show a contradiction in set theory.
Which does not exist outside of WM's wild weird world of WMytheology. > > > > You might Not be able to, and in fact CAN'T Define that Bijection needed to > > show the Set is Countable. > > But I can prove
Not outside of WM's wild weird world of WMytheology. > > > > > > There is NO Formula that Defines ALL the Reals that are Definable by a > > Formula! > > Of course. There are not *all* reals.
There are outside of outside the wild weird world of WMytheology. > > > However, then we can Prove that there Exists an Undefinable Real Number. > > No, you cannot, and nobody has ever done it.
It is quite possible to prove the existence of real numbers which do not have any finite definition, but are only defined collectively, i.e., as members of sets.
Note that every set has more subsets than members, so that even the set of all finite definitions must have subsets that, as individual objects, cannot be finitely defined. --