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**sfspitfire23** Q- Prove that the collection of all finite subsets of N are countable

What I have so far:

Let $\displaystyle A_i$ be the set of all subsets of $\displaystyle \mathbb{N}$ consisting of $\displaystyle i$ elements, $\displaystyle A$ be the set of all finite subsets of $\displaystyle \mathbb{N}$. Then $\displaystyle A$ is a union of $\displaystyle A_i$....

Now I need to find a bijective function of this union to the real numbers? How should I proceed from where I am?

Thanks