Discrete math problem

[krypic]

How would I begin to show that if
A~N then AxA~N

 

[pka]

How would I begin to show that if
A~N then AxA~N

Because \(A\sim\mathbb{N}\) there is a bijection \(f: A\to \mathbb{N}\).
If \((x,y)\in A\times A\) then \((\exists n_x\in\mathbb{N})\wedge (\exists n_y\in\mathbb{N})[f(x)=n_x\wedge f(y)=n_y]\)
Now define \(A\times A\to\mathbb{N}\times\mathbb{N}\) by \(\Phi[(x,y)]=(n_x,n_y)\)
Can you finish?