In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 2 Jul., 04:03, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > > My answer to your question above is similar. The question whether a > > countable > > union of countably many sets is countable is implied by the axiom of > > countable > > choice, which is not provable from ZF. So negating the axiom of countable > > choice (which implies negating the axiom of choice) we can have situations > > where the conclusion is false. > > Feferman and Levy showed that the statement that the set of all real > numbers is the union of a denumerable set of denumerable sets cannot > be refuted.
Based on what set of axioms? > > So does it depend on the chosen axioms, whether R is countable?
Everything in formal Math depends on sets of axioms.