Originally Posted by

**Neutriiino** This is a problem I'm having a hard time solving:

Let $\displaystyle P(\mathbb{N})$= the power set of $\displaystyle \mathbb{N}$ and for every natural number, n, $\displaystyle P(\mathbb{N}_n)$ be the power set of $\displaystyle \mathbb{N}_n$ which is a **finite **subset of $\displaystyle \mathbb{N}: \mathbb{N}_n=\left \{ 1,2,3,...,n \right \}$.

Now, if for every n, $\displaystyle A_n=P(\mathbb{N})-P(\mathbb{N}_n)$,

what can be said about $\displaystyle \bigcap_{n=1}^{\infty }A_n?$

Is that an infinite subset of $\displaystyle \mathbb{N}$?