On Sunday, 4 May 2014 00:32:08 UTC+2, Zeit Geist wrote: > 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. >
Here we talk about mathematics performed in English. There definable and uncountable exclude each other, not only "in a certain way".