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Topic: My set theory
Replies: 6   Last Post: Apr 7, 2014 7:32 AM

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Aatu Koskensilta

Posts: 2,638
Registered: 6/28/08
Re: My set theory
Posted: Apr 4, 2014 2:44 PM
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Peter Percival <peterxpercival@hotmail.com> writes:

> I think that in a theory of sets without the axiom of choice there can
> be non-comparable cardinalities.


Sure. But even in such theories the inequality |N| < |R| will hold,
witnessed by the injection taking the natural n to the real n.

--
Aatu Koskensilta (aatu.koskensilta@uta.fi)

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



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