As is GCH

Axiom of choice seems inherently reasonable until you hit things like Banach-Tarski. CH says there is nothing bigger than the rationals but smaller than the reals which "feels right".

Posted By: Partial Angler on May 11th 2009 at 11:25:21

Message Thread

The coastline of Africa - the world's 2nd largest continent - is shorter than that of Euro (General Chat) - Ralf Scrampton, May 11, 09:39:45
- They are both infinite in some sense (General Chat) - yarmyyarmy, May 11, 10:40:17
  - Sod that. Get your My First World Atlas. Some string, some pins, and measure it (General Chat) - Yellalee, May 11, 10:49:30
  - it is still possible to have one infinite bigger than another infinite. (General Chat) - Ralf Scrampton, May 11, 10:47:48
    - You're thinking about alephs - aleph-one being "bigger" than aleph-null. (General Chat) - Arizona Bay, May 11, 10:51:59
      - The Continuum Hypothesis asks whether there is an order of infinity between (General Chat) - yarmyyarmy, May 11, 11:02:18
      - perhaps that's what i'll learn tonight (General Chat) - Ralf Scrampton, May 11, 10:58:02
        
        Rationals are countable but reals aren't (General Chat) - Partial Angler, May 11, 11:41:24
    - Georg Cantor (General Chat) - yarmyyarmy, May 11, 10:51:40
      - Oh please say the Wrath is going to get all Fundamentals of Set Theory. (General Chat) - Arizona Bay, May 11, 10:53:58
        
        Cantor's Continuum Hypothesis... (General Chat) - Basil Wrathbone, May 11, 10:59:52
        
        As is GCH (General Chat) - Partial Angler, May 11, 11:25:21
- Fjords. (n/m) (General Chat) - Arizona Bay, May 11, 10:18:41
  - Norway has the second longest coastline in the world (General Chat) - Ralf Scrampton, May 11, 10:23:59
    - ... (General Chat) - SCC 28, May 11, 10:38:37
      - What about scroby sands? (n/m) (General Chat) - Partial Angler, May 11, 11:28:31
      - perhaps, unless it hasn't, i think i read that in Frost on my Moustache (n/m) (General Chat) - Ralf Scrampton, May 11, 10:40:59

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