In article <email@example.com>, firstname.lastname@example.org wrote:
> On Sunday, 4 May 2014 23:52:40 UTC+2, Zeit Geist wrote: > > > > > No I claim that a countable set has only countable or finite subsets. > > > > > > > > True, a Subset of a Set Cannot exceed the Cardinality of that Set. > > > > > > > > However, your Set of Finite Definitions is Not Countable. > > > > > So, how do find the Set of Definable Real is Countable? > > It is a subset of the countable set of all finite expressions.
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.
It is for a similar reason that while the individualy defineable reals are countable, there are reals which are not individually defineable.
In fact, every defineable real interval of positive length (defined by its endpoints) contains uncuntably many of them.
At least everywhere outside of WM's wild weird world of WMytheology. --