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Prove A is countable

  1. Dec 9, 2013 #1
    Let A be the set of all real numbers in the interval [7,8) that have only 5 and 7 in their decimal expansion. A is defined by

    A:={7.a1a2a3|ai ε {5,7} for all i ε [itex]\aleph[/itex]}

    Prove A is countable.
     
  2. jcsd
  3. Dec 9, 2013 #2
    ... Are you sure that's true?

    Can you show that [itex]A[/itex] is the same size as [itex]\{S: \enspace S\subseteq \mathbb N\}[/itex]? Is the latter countable?
     
  4. Dec 9, 2013 #3

    tiny-tim

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    hi giro! welcome to pf! :wink:

    show us what you've tried and where you're stuck, and then we'll know how to help :smile:
     
  5. Dec 9, 2013 #4

    Mark44

    Staff: Mentor

    tiny-tim and economicsnerd,
    When you see a post like this, that is pretty obviously a homework assignment, please use the Report button so that a mentor can deal with it.
     
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