My Math Forum newbie axiom of choice

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 June 30th, 2010, 09:50 AM #1 Member   Joined: Apr 2010 Posts: 54 Thanks: 0 newbie axiom of choice Principle of Well-ordering: Every set can be well-ordered (that is, there exists for any set a total-order such that any subset has a smallest element). Axiom of choice: Every set has a choice function (a function that assigns to each non-empty subset of the given set an element of the subset). I need to prove that the Princ. of Well-Ordering implies the Axiom of choice. This is my proof: Let X be a set. Apply a well-ordering to it. Define a function that assigns to each non-empty subset A of X the smallest element of A. This is a choice function. I think that's ok, but I want to be sure. So, is it ok? Thanks.
 June 30th, 2010, 10:06 AM #2 Senior Member   Joined: Jun 2010 Posts: 618 Thanks: 0 Re: newbie axiom of choice Hi becko. Your argument is fine. That's exactly how it's done.
 June 30th, 2010, 08:15 PM #3 Member   Joined: Apr 2010 Posts: 54 Thanks: 0 Re: newbie axiom of choice thanks

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