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June 30th, 2010, 09:50 AM   #1
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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.
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June 30th, 2010, 10:06 AM   #2
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Re: newbie axiom of choice

Hi becko.

Your argument is fine. That's exactly how it's done.
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June 30th, 2010, 08:15 PM   #3
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Re: newbie axiom of choice

thanks
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