I have the set:  

$$\Bbb N \cup \{(i, j) \in \Bbb N^2| i \le j\}$$  

I don't really understand the meaning of $\Bbb N^2$.  

I think I would have $\Bbb N \cup {(0,0), (0,1), ... (1,1), (1,2)...(n,n)}$  

Which would be exactly $\Bbb N$ and the $\Bbb N^2$ would be useless. But I dont get why won't they just put $\Bbb N$ instead.