03-00-ExampleOfBijection.tex

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\pmtitle{example of bijection}
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\begin{document}
It is known that the Cartesian product of numerable sets are numerable, then the product $\mathbb{N}\times\mathbb{N}$ is. Here we give an explicit mapping which does the task:
$$(n,m)\mapsto m+\frac{(n+m)(n+m+1)}{2}$$
It is almost easy to check bijectivity and curious how the elements of $\mathbb{N}\times\mathbb{N}$ are labeled.
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