# Axiom of Choice - Naive Counterexample [duplicate]

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Axiom of choice question

I know there is a lot of discussion on the axiom of choice and, in fact, I attended once a lecture on it, but I still cannot understand the following: Let $A$ be a nonempty set. I want to pick an element from $A$. Since by hypothesis $A$ is nonempty, it must contain at least one element, $a$. So I pick this $a$. Where is the "gap" or the need for the axiom of choice?

## marked as duplicate by Cameron Buie, Carl Mummert, Chris Eagle, Ross Millikan, Thomas AndrewsDec 11 '12 at 20:39

• It's not even clear why you call this a "counter-example," since it is an example of choice working (although an example that doesn't need the Axiom of Choice to work.) – Thomas Andrews Dec 11 '12 at 20:40