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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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Aatu Koskensilta

Posts: 1,982
Registered: 12/6/04
Re: How many real numbers are there?
Posted: Jul 8, 2006 8:53 AM
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Toni Lassila wrote:
> On 7 Jul 2006 13:30:05 -0700, "Nathan" <> wrote:

>> Mike Deeth wrote:

>>> It's well-known that a countable union of finite sets is countable.
>> Nope! You said you were working in ZF. This requires AC.
> No it doesn't.

Sure it does. The reals can be a countable union of countable sets if AC
fails, omega_1 can have cofinality omega; all sorts of interesting stuff
can happen in the absence of AC.

Aatu Koskensilta (

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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