Bijection between $\mathbb{N}^2$ and $\{(x, y) \in \mathbb{N}^2: x \geq y\}$.
My idea is to walk diagonally on $\mathbb{N}^2$, starting from $(0, 0)$, then to $(1, 0)$, $(0, 1)$ etc. Hopefully I can then match them to the "triangle" on $\{(x, y) \in \mathbb{N}^2: x \geq y\}$. I don't know how to formalise it but I think the idea is possible.
Please instruct me in how I can mathematically write this. Thanks.