# Prove that co finite set over N is countable [duplicate]

I have $$L = \{A \in \mathcal P(\mathbb N) | A \text{ co finite over } \mathbb N\}$$

How can I prove that $L$ is countable?

Thanks

• I've edited your post to format the math in it. Please verify that it says what you intended. – user61527 Apr 28 '14 at 5:35
• Note there is a canonical bijection between the set of finite subsets, and the set of cofinite subsets. – Asaf Karagila Apr 28 '14 at 5:36

Hint: Find a bijection $$\{ A \in \mathcal{P}(\mathbb{N}) : A\ \text{cofinite} \} \longleftrightarrow \{ A \in \mathcal{P}(\mathbb{N}) : A\ \text{finite} \}$$ and use familiar facts about countable sets to deduce that the latter, hence the former, is countable.