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Cardinality of the set of all ordinals.

  1. Feb 6, 2013 #1
    What would the cardinality of the set of all ordinal numbers be? Is it even known or does the question even make sense in the case of such a weird, almost paradoxical set?
     
  2. jcsd
  3. Feb 6, 2013 #2

    micromass

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    The class of all ordinals doesn't form a set. There are simply too many ordinals to enclose them all in a set. Rather, the class of all ordinals forms a proper class. In ZFC set theory, there is no way to assign a cardinality to a proper class.

    This should be interesting for you: http://en.wikipedia.org/wiki/Burali-Forti_paradox
     
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