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For school, I have to prove that every finite subset of $\mathbb N$ is countable. Wikipedia tells me, that "By definition a set $S$ is countable if there exists an injective function $f$ from $S$ to the natural numbers.". I'm probably missing something obvious here, but why is this true?

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    @percusse OK thanks! I somehow didn't see that you are assigning elements from $\mathbb{N}$, but now it makes sense. Thanks!2011-10-08

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If it is a set with finite number of elements, you can exhaust its elements by simply assigning elements from $\mathbb{N}$. This is a special case of the definition : A set $S$ is countable if and only if there exists a one-to-one correspondence with a subset of natural numbers.