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Cardinality question

  1. Nov 17, 2009 #1
    Need help with this proof:
    Prove that the set of irrational numbers has the same cardinality as the set of real numbers.
     
  2. jcsd
  3. Nov 17, 2009 #2

    Office_Shredder

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    I would do this by a bijection. Pick a countable set A in the irrational numbers (think cosets if you can't come up with an example). Then construct a bijection that is the identity outside of A
     
  4. Nov 17, 2009 #3

    Hurkyl

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    I would use arithmetic of cardinal numbers myself.
     
  5. Nov 17, 2009 #4

    statdad

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    The reals are the disjoint union of rationals and irrationals. Take this back to Hurkyl's suggestion.
     
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