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How can one prove

  1. Feb 28, 2006 #1

    dextercioby

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    that the number of elements of [itex] \mathbb{R} [/itex] (seen as a set, obviously) is bigger than the number of elements of [itex] \mathbb{N} [/itex] ...? :bugeye:

    Daniel.
     
  2. jcsd
  3. Feb 28, 2006 #2

    George Jones

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    Two sets have the same cardinality iff there exists a bijection between the sets. Cantor showed that there is no bijection between [itex]\mathbb{R}[/itex] and [itex]\mathbb{N}[/itex]. A cool proof of this involves a very simple idea - simple once one has seen it, but not until then.

    Regards,
    George
     
  4. Mar 1, 2006 #3

    dextercioby

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    Thankyou for the reply.

    Daniel.
     
  5. Mar 1, 2006 #4
    Very nice. I've never seen that proof before.
     
  6. Mar 1, 2006 #5
    Wow...that's good!
     
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