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Set of all rational sequences countable?

  1. Nov 6, 2011 #1
    I know that Q (rational numbers) are countable and that the finite cartesian of Q with itself, Q^n is countable but is it true that the countably infinite cartesian product of Q with itself is countable? The set of all rational sequences are isomorphic to Q^∞ (here im saying Q^∞ is the countable cartesian product of Q with itself) so if I know Q^∞ is countable then I know the set of all rational sequences is countable. I need this result to prove something else for a hw problem and I want to be able to justify it.
  2. jcsd
  3. Nov 6, 2011 #2


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    Think about the real numbers.
  4. Nov 6, 2011 #3
    ah nevermind I see it. Thank you I was wrong.
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