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How does one get the formula for this bijection from $\mathbb{N}\times\mathbb{N}$ onto $\mathbb{N}$?
I have seen analysis books that show $\mathbb{N}\times \mathbb{N}$ is countable by "walking along the diagonals" argument. But I was never quite sure why is this enough, as this does not give a specific rule (or formula) for each element in $\mathbb{N}\times \mathbb{N}$ (which certainly can be constructed in the first place). I hope this question makes some sense..