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How is uncountability characterized in second order logic?

  1. Jun 10, 2012 #1
    How is uncountability characterized in second order logic?
     
  2. jcsd
  3. Jun 20, 2012 #2
    A set is infinite if it can be put in one-to-one correspondence with one of its proper subsets. A set is countably infinite if it is infinite and it can be put in one-to-one correspondence with every one of its infinite subsets. A set is uncountably infinite if it is infinite but not countably infinite.
     
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