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### show that the set of all 2-element subsets of $\mathbb{N}$ is countable [duplicate]

show that the set of all 2-element subsets of $\mathbb{N}$ is countable could someone guide me through this problem?
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### 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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### Set of all finite subsets of $\mathbb{N}$ is a countable set [duplicate]

Possible Duplicate: Show that the set of all finite subsets of $\mathbb{N}$ is countable. How can I prove in a proper way that the "set of all finite subsets of $\mathbb{N}$ (the set of natural ...
It is known that $|2^\Bbb{N}|=|\Bbb{R}|$ and that $2^\Bbb{N}$ contains all the subsets of $\Bbb{N}$, just an idea of a question I had and that I would like suggestions on how to tackle. My question ...