On 19 Mai, 13:31, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > WM <mueck...@rz.fh-augsburg.de> writes: > > On 19 Mai, 05:06, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > >> Let's talk > >> about theorems of ZFC. > > > ZFC: There are countably many rationals and uncountably many > > irrationals in (0, 1). > > > Now cover every rational with an interval, namely the n-th rational > > q_n with an interval of measure 10^-n. Then you cover 1/9 (or less) of > > the unit interval with aleph_0 intervals. In the remaining 8/9 (or > > more) there are uncountably many irrationals. But every two > > irrationals have a rational between each other. That implies in the > > present example, they have even a finite interval between each other, > > because there are no rationals outside of intervals. So we have > > uncountably many irrationals separated by countably many rationals. > > Contradiction. > > Well, so much for talking about theorems of ZFC, eh?
I knew you would not talk to the topic - as usual when your "logic" is exhausted. But perhaps other read it and wonder how that could be. > > > Usually there is some blathering about "Cantor-dust" in the reply. But > > even elements of Cantor-dust must be separated by intervals around > > rational numbers. > > Quite right. You've proved ZFC is inconsistent and them mean ol' > mathematicians ignore you.
You are in gross error. *Matheologicans* must ignore that because they cannot refute it and they cannot accept it either without losing their ideology and, in many cases, their occupation. Mathematicians know: Every sentence that starts with the phrase "For all natural numbers" is false.