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Cantor diagonalization argument

  1. Feb 19, 2009 #1
    sorry for starting yet another one of these threads :p

    As far as I know, cantor's diagonal argument merely says-

    if you have a list of n real numbers, then you can always find a real number not belonging to the list.

    But this just means that you can't set up a 1-1 between the reals, and any finite set.

    How does this show there is no 1-1 between reals, and the integers?
     
  2. jcsd
  3. Feb 19, 2009 #2

    CRGreathouse

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    No. It says that if you have a countable list of real numbers, you can form one that isn't anywhere on the list.
     
  4. Feb 19, 2009 #3

    HallsofIvy

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    Crucial point being "countable" not "n". So there is "no 1-1 between reals, and the integers". Cantor's "list" is not finite.
     
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