Jonathan Hoyle wrote: > <most of rant snipped> > > is countable. Let r be a real number. By our above observations, r is > > just some ZF set, and hence r in S_i for some i, hence S in T. > > (snip) > > You appear to be confusing the theory (ZFC) with your model (R). You > realize that ZFC does have both countable and uncountable models, don't > you? > > Jonathan Hoyle
Nowhere in the constructions of the real numbers do we make any assumptions that we are in some exotic set theory with supernatural powers. This is not X-Men mathematics! The set T which I contructed in my original post satisfies all the axioms of ZF and therefore the contructions of the reals work fine therein. For those who naysay because of choice, it would be trivial to alter my definition to include that as well. Please stop picking on strawmen and admit the deep flaw in the Cantor Cabal.
Very humbly and sincerely your friend, Nathan Deeth Age 11 :-)