I need to prove that powers are equivavalent.
$$\mathbb{N}^{\mathbb{N}\times Q} \times \mathbb{N} \sim R^Q$$
Well, $\mathbb{Q} \sim \mathbb{N}$ and $\mathbb{N} \times \mathbb{N} \sim \mathbb{N}$.
We now have to prove this $$\mathbb{N}^{\mathbb{N}} \times \mathbb{N} \sim R^\mathbb{N}$$
What to do next? Probably use cantor-bernstein theorem??
