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Quick question about cardinals

  1. Aug 22, 2007 #1
    Assuming we define the cardinal number for a set A as the least ordinal number b such that A and b are equipollent, how would you define an uncountable set of cardinal numbers?
     
  2. jcsd
  3. Aug 22, 2007 #2

    matt grime

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    It's just an uncountable set. That it happens to be a set of cardinals is immaterial.
     
  4. Aug 22, 2007 #3
    What I mean is that under this model every set of cardinals "up to x" seems to be countable. So how to define an uncountable one?
     
  5. Aug 22, 2007 #4

    matt grime

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    How does that imply that all cardinals are countable? Why not post a proof of that statement if it 'seems' to be so. Hint, let w be an uncountable ordinal. Such exist. It is not in bijection with any countable initial segment, so it must define an uncountable cardinal too.
     
    Last edited: Aug 22, 2007
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