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
Canonical name	ExampleOfBijection
Date of creation	2013-03-22 16:30:18
Last modified on	2013-03-22 16:30:18
Owner	juanman (12619)
Last modified by	juanman (12619)
Numerical id	7
Author	juanman (12619)
Entry type	Example
Classification	msc 03-00
Related topic	ParingFunction