Here is the problem. Prove that

^{\mathbb{Z^+}}\mathcal{P}(\mathbb{Z^+})\sim \mathcal{P}(\mathbb{Z^+})

Where ^{\mathbb{Z^+}}\mathcal{P}(\mathbb{Z^+}) means the set of
functions from \mathbb{Z^+} to \mathcal{P}(\mathbb{Z^+}).

So I have to come up with some kind of bijection between the two sets. Anything
which belongs to \mathcal{P}(\mathbb{Z^+}) is a subset of
\mathbb{Z^+}. I will need to associate this to some function from
\mathbb{Z^+} to \mathcal{P}(\mathbb{Z^+}).

I am having difficulty coming up with such a bijection. Is it too difficult?. Or is there another approach to tackle this problem ?