# What is the cardinality of a set of all finite subsets of $\Bbb{N}$? [duplicate]

I'm looking for cardinality of $P_{fin}(\Bbb{N})=\{x|x\subset\Bbb{N}$ and $x$ finite$\}$. I was told in my classes that it's $\aleph_0$, but how to prove it?

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• Show there is a bijection between $P_{fin}(\mathbb N)$ and $\mathbb N$. – davcha Jan 27 '15 at 9:41
Hint: Show that there is a natural bijection between $P_{\text{fin}}(\mathbb{N})$ and $\mathbb{N}$; one particularly nice one is more apparent when you work in binary.