How one can embedding $P(\mathbb{N})$ into $P_{\infty}(\mathbb{N})$, where $P_{\infty}(\mathbb{N})=\{A\in P(\mathbb{N})\ \ : \ \ A \ \ \ \text{is infinit set} \}$?
I've tried defining a following function, $f:P(\mathbb{N})\to P_{\infty}(\mathbb{N}) $, as:
$f(A)=\mathbb{N}\setminus A$
But there is a problem when $A=\mathbb{N}$
Thank you.