The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Eric Schmidt

Posts: 24
Registered: 7/7/06
Re: How many real numbers are there?
Posted: Jul 7, 2006 8:44 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

>>
>>(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.


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

--
Posted via a free Usenet account from http://www.teranews.com




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.