On Saturday, May 3, 2014 2:04:34 PM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Saturday, 3 May 2014 20:55:10 UTC+2, Virgil wrote: > > > There is only one such set which has no elements. the empty set, > > What elements has the set of all individually undefinable real numbers? Does it differ from one of its subsets by applying the axiom of extensionality?
Depends on the Model you're working in.
If it is Non-Empty, then it differs from All but One of its Subsets.
Of course, in L ( Gödel's Constructable Universe ) All Reals are "Definable" in a certain way. And yet, they remain Uncountable in L.