> On 19 Mai, 05:06, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: >> WM <mueck...@rz.fh-augsburg.de> writes: >> > On 19 Mai, 00:12, William Hughes <wpihug...@gmail.com> wrote: >> >> On May 18, 2:47 am, Virgil <vir...@ligriv.com> wrote: >> >> >> > In article >> >> > <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>, >> >> >> > WM <mueck...@rz.fh-augsburg.de> wrote: >> >> > > God knows a list of all natural numbers [*]. >> >> >> > Anyone who uses a claimed "God" to justify his mathematics is far more >> >> > priest than mathematician. >> >> > -- >> >> >> Well, the use of the term "God" is harmless. I often talk >> >> about "God's Algorithm" to refer to a desirable but impractical >> >> way to a result. No theism is implied. >> >> > But Cantor's finished infinity and list of all reals implies theism. >> >> Right. >> >> Sure it does. >> >> Tell you what. Let's change the subject ever so slightly. 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?
> 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. My, oh my!
-- "I told her that I loved her. She said she loved me too. Neither one was lying, Yet it wasn't true." -- Del McCoury Band