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#### OhMyMarkov

##### Member

- Mar 5, 2012

- 83

I want to show that all countable sets are closed. I can show that finite sets are closed, and the set of all natural numbers is closed by showing its complement to be a union of open sets. Now, can I start like this:

A is a countable set. Every element in A can be "mapped" to an element in N by the property of countability (I presume). N is finite, so A is finite too.

Is there proof correct, if it is but technically incorrect, could you suggest a better proof.

Thanks!