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Math Help - Choice functions

  1. #1
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    Choice functions

    Find, if possible, a choice function for each of the following collections without using the axiom of choice.

    (a) The collection A of nonempty subsets of Z+
    (b) The collection B of nonempty subsets of Z

    There are a (c) and (d) as well, but I am hoping that help with these first two will mean I can do the last two.

    I do not know how to do this. If someone could explain the process and also give a little more in depth explanation of a choice function, it would really help me.

    Thanks!
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  2. #2
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    Z+ and Z are well-ordered. That means every subset has a least element. There's your choice function. Take the least element of each set.
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  3. #3
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    Here is a very good website on The Axiom of Choice .
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