Toni Lassila wrote: > On 7 Jul 2006 13:30:05 -0700, "Nathan" <email@example.com> wrote: > >> Mike Deeth wrote: >> >>> It's well-known that a countable union of finite sets is countable. >> Nope! You said you were working in ZF. This requires AC. > > No it doesn't.
Sure it does. The reals can be a countable union of countable sets if AC fails, omega_1 can have cofinality omega; all sorts of interesting stuff can happen in the absence of AC.
-- Aatu Koskensilta (firstname.lastname@example.org)
"Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus