How do I start this? Do I follow the same proof on why rational numbers are countable?
2026-04-05 01:58:55.1775354335
Deduce that $\mathbb Q^n$ is countable for any integer $n \in \mathbb N$
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Yes. First of all you may replace $\mathbb Q^n$ with $\mathbb N^n$ and then use induction: $\mathbb N^{n+1}\cong \mathbb N\times \mathbb N^n\cong \mathbb N\times \mathbb N\cong \mathbb N$