Set of all rational sequences countable?

  • Thread starter rat bass
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  • #1
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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.
 

Answers and Replies

  • #2
pwsnafu
Science Advisor
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Think about the real numbers.
 
  • #3
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ah nevermind I see it. Thank you I was wrong.
 

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