Show that B is a Boolean subalgebra of $\mathbb{P(N)}$ which cannot be Boolean isomorphic to some $\mathbb{P(M)}$

Question

Let $B = \{X \subseteq \mathbb{N} | X $ is finite or its complement $ \subseteq \mathbb{N}$ is finite$\}$. Show that B is a Boolean subalgebra of $\mathbb{P(N)}$ which cannot be Boolean isomorphic to some $\mathbb{P(M)}$.

Answer 1

You should show yourself that it is a Boolean algebra. $B$ cannot be Boolean isomorphic to the power set of some set because the former is countably infinite and the latter is either finite of uncountable.