POV-Ray : Newsgroups : povray.off-topic : Random wonderings 0x20c26764ae15b956c9a5eb7c1a237639 : Re: Random wonderings 0x20c26764ae15b956c9a5eb7c1a237639 Server Time
3 Sep 2024 17:19:18 EDT (-0400)
  Re: Random wonderings 0x20c26764ae15b956c9a5eb7c1a237639  
From: Darren New
Date: 8 Mar 2011 13:07:41
Message: <4d76706d$1@news.povray.org>
Roman Reiner wrote:
>> Yep. There's really only two infinities you get when you talk about
>> "numbers" - Aleph0 and Aleph1.
> 
> Wasn't the question whether there is a set that is larger than a countable
> infinite set and smaller than an uncountable infinite set proven to be
> unprovable?

My memory is that it was thought to be unprovable but later proven to not be 
so. However, wikipedia (Cardinal_numbers) agrees with you. Not that it's 
unprovable, but that its provability depends on the axioms of set theory you 
accept. I suspect it depends in part on things like the axiom of choice, etc.

-- 
Darren New, San Diego CA, USA (PST)
  "How did he die?"   "He got shot in the hand."
     "That was fatal?"
          "He was holding a live grenade at the time."


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