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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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Jonathan Hoyle

Posts: 754
Registered: 12/10/04
Re: How many real numbers are there?
Posted: Jul 7, 2006 5:00 PM
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<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
you?

Jonathan Hoyle




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