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Re: Mathelogy S 011
Posted:
May 19, 2012 7:56 AM
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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.
Regards, WM
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