June 30th, 2010, 09:50 AM  #1 
Member Joined: Apr 2010 Posts: 54 Thanks: 0  newbie axiom of choice
Principle of Wellordering: Every set can be wellordered (that is, there exists for any set a totalorder such that any subset has a smallest element). Axiom of choice: Every set has a choice function (a function that assigns to each nonempty subset of the given set an element of the subset). I need to prove that the Princ. of WellOrdering implies the Axiom of choice. This is my proof: Let X be a set. Apply a wellordering to it. Define a function that assigns to each nonempty 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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