# example of bijection

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.

Title example of bijection ExampleOfBijection 2013-03-22 16:30:18 2013-03-22 16:30:18 juanman (12619) juanman (12619) 7 juanman (12619) Example msc 03-00 ParingFunction