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Topic: How many real numbers are there?
Replies: 18   Last Post: Jul 9, 2006 3:00 PM

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Eric Schmidt

Posts: 24
Registered: 7/7/06
Re: How many real numbers are there?
Posted: Jul 7, 2006 8:44 PM
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Mike Deeth wrote:
> 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.

>>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
>>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.

You have not proved that every set (or even every real number) is in
some S_i. In fact, you yourself construct a set not in any S_i, namely
T. Therefore you have not found any flaw in set theory.

Your mistake is thinking all real numbers are constructible.

Eric Schmidt

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