Question

Prove that the set
\[A=\left\{ (m,n)\in \mathbb{N}\ x\ \mathbb{N}:\ m \le n \right\}\]
is countably infinite.

Answer 1

infinite of what order

Answer 2

(1,1)->1
(1,2)->2
(2,2)->3
(1,3)->4
(2,3)->5
(3,3)->6
...

Answer 3

\[f(m,n):=\frac{n(n-1)}{2}+m\]