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How do I start this? Do I follow the same proof on why rational numbers are countable?

Hagen von Eitzen
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Howlett
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  • By $\mathbb{Q}^n$, do you mean an $n$-tuple of rationals? – Brian Tung Sep 05 '15 at 22:09
  • Start by making the body of the Question as self-contained as possible, so that the title does not bear the entire burden of problem statement. Consider using the "proof on why rational numbers are countable" as a basis step for proof of the wider proposition by induction. – hardmath Sep 06 '15 at 01:13

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Yes. First of all you may replace $\mathbb Q^n$ with $\mathbb N^n$ and then use induction: $\mathbb N^{n+1}\cong \mathbb N\times \mathbb N^n\cong \mathbb N\times \mathbb N\cong \mathbb N$

Hagen von Eitzen
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