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?