On Sunday, May 4, 2014 11:24:10 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Sunday, 4 May 2014 19:29:04 UTC+2, Zeit Geist wrote: > > > You also ignore the Definition of Countability in this Context and the Fact that No Definable Bijection Exist between your Set of Definitions and the Natural Numbers. > > 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! You might Not be able to, and in fact CAN'T Define that Bijection needed to show the Set is Countable.
There is NO Formula that Defines ALL the Reals that are Definable by a Formula!
You may Assume that there is. No Axiom of ZFC will be Viotated. However, then we can Prove that there Exists an Undefinable Real Number.