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Recently, in an answer to a question I posted on this website, I've been advised to use $\mathbb{N} \cong \mathbb{N}^{2}$. The problem is I haven't been able to prove it, as I've only been able to find injective functions from $\mathbb{N}$ to $\mathbb{N}^{2}$ and have been struggling with finding a bijective one.
Any help with the proof will be much appreciated. Thanks in advance!

tcb93
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    As a general note: to prove that two sets have the same cardinality, it is generally easier to exhibit two injections (one from $A\to B$, the other from $B\to A$). Explicit bijections are sometimes hard to write down (though the duplicate gives a typical bijection in this particular case). – lulu Jul 30 '22 at 09:44
  • It seems strange to mark as a duplicate of a closed question. – Suzu Hirose Jul 30 '22 at 09:51
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    @SuzuHirose I agree, but (among other good answers) it contained an explicit bijection, which I thought the OP might want, and of course it contained links to other duplicates. I've noticed that some people seem to be able to closed a duplicate question while pointing to multiple duplicates (in the Closure notice I mean, not in the comments). I don't know how to do that, nor do I know if that is something every user can do. – lulu Jul 30 '22 at 09:55
  • here is another duplicate, but I think the answers for the prior one are more informative. – lulu Jul 30 '22 at 09:57

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