Would the powerset of $\mathbb{Z}$ also not denumerable?

Question

Would the powerset of $\mathbb{Z}$ also be not denumerable?, Since Cantor's theorem says that the $\mathbb{N}$ is denumberable but the powerset of $\mathbb{N}$ is not denumberable because there does not exist a surjective function from $\mathbb{N} \rightarrow$ $P( \mathbb{N} )$

I feel like this should be true for $\mathbb{Z}$ as well am I wrong?

Answer 1

Since $\mathbb Z$ and $\mathbb N$ have the same cardinality, so do $P(\mathbb Z)$ and $P(\mathbb N)$.