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[parent] example of bijection (Example)

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.




"example of bijection" is owned by juanman.
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See Also: pairing function


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Cross-references: elements, mapping, product, numerable sets, Cartesian product

This is version 4 of example of bijection, born on 2006-12-24, modified 2006-12-24.
Object id is 8680, canonical name is ExampleOfBijection.
Accessed 1973 times total.

Classification:
AMS MSC03-00 (Mathematical logic and foundations :: General reference works )

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