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Cardinality of sets

  1. Mar 16, 2009 #1
    The cardinality of set of [N][tex]\omega[/tex] . what does omega stands for?
  2. jcsd
  3. Mar 17, 2009 #2
    This seems a bit out of the blue, I never seen something like that but could it by any chance be referring to [itex]X^Y=\{f : Y \rightarrow X \}[/itex] ?
  4. Mar 17, 2009 #3

    matt grime

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    The lower case omega is (usually) the first infinite ordinal.
  5. Mar 17, 2009 #4
    so is omega the same as aleph not. and in this case it would be aleph not to the power aleph not which gives aleph not?
  6. Mar 18, 2009 #5


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    omega's cardinality is aleph naught. But omega is an ordinal, while aleph naught is a cardinal.
  7. Mar 18, 2009 #6
    It's an infinite sequence of natural numbers.
  8. Mar 18, 2009 #7


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    Usually the notation [itex][N]^{\omega}[/itex] denotes the collection of subsets of N of size [itex]\omega[/itex], i.e.:

    [tex][N]^{\omega} = \{ X \subseteq N : |X| = \omega \}[/tex]
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