Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


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

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Aatu Koskensilta

Posts: 2,638
Registered: 6/28/08
Re: My set theory
Posted: Apr 7, 2014 7:32 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Virgil <virgil@ligriv.com> writes:

> In article <87wqf5oryn.fsf@uta.fi>,
> Aatu Koskensilta <aatu.koskensilta@uta.fi> wrote:
>

>> 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.

>
> That would certainly justify |N| <= |R|, but why would it necessitate
> strict inequality?


By the uncountability of the reals. In any case, this more or less
trivial injection -- the identity map, morally speaking -- suffices to
establish comparability.

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

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



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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.