Show that N$2$ :$=$ N $\backslash$times N $=\{($m$,$ n$)$ : m$,$ n in N$\}$ is countably infinite.

Using the principle of mathematical induction, show that Nd is countably infinite for each d in N$.$

Hint: For the case n $=2,$ consider g : N $\backslash$times N $->$ N defined as g$($m$,$ n$)=($m $+$ n$)2+$ n$.$ Argue that g is bijective.