On Sunday, 4 May 2014 01:12:40 UTC+2, Virgil wrote:
> > What elements has the set of all individually undefinable real numbers? >
> All but the countably many real numbers for which there can be finite > individual definitions.
> > Does > > it differ from one of its subsets >
> It only need differ from its proper subsets, of which there are many. >
> E.g., EVERY subset of only those individually undefinable real numbers > within a real interval having distinct rational endpoints will be a > proper subset of the set of all individually undefinable real numbers.
And without rational endpoints? Take the well-ordered set of all undefinable real numbers, then remove 10 elements. How can you do so by applying the axiom of extensionality?