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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 ]
Jonathan Hoyle

Posts: 754
Registered: 12/10/04
Re: How many real numbers are there?
Posted: Jul 7, 2006 5:00 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

<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.

Your "hence" is a false deduction. You have not shown that r is S_i
for some i. You seem to be assuming that T exhausts all ZF sets, which
is not necessarily true. All you have is T containing all sets which
can be constructed in a finite number of steps. You have not disproven
the existence of sets which cannot be constructed in this matter.

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

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 1994-2018. All Rights Reserved.