Re: How many real numbers are there?


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 :-)

.