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Is set of points (p,q) countable?

  1. Jun 20, 2009 #1
    I want to show that the set of points (p,q) on the plane with rational coordinates p and q is countable. I proved set of rational numbers is countable by drawing table and I find (http://web01.shu.edu/projects/reals/infinity/proofs/combctbl.html ) Combining Countable Sets. However, I cannot put these together in table.
    Could it be proven by matematically instead of table drawing?
     
    Last edited by a moderator: Apr 24, 2017
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  3. Jun 20, 2009 #2

    CRGreathouse

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    If you know how to prove that there are only countably many rationals, the proof is exactly the same.
     
  4. Jun 20, 2009 #3

    HallsofIvy

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    For that matter, since you have proven that there are only countably many rationals, any subset of the rationals is either finite or countable.
     
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