• sushibowl@feddit.nl
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    6 months ago

    It seems to me that, since the set of real numbers has a total ordering, I could fairly trivially construct some choice function like “the element closest to 0” that will work no matter how many elements you remove, without needing any fancy axioms.

    I don’t know what to do if the set is unordered though.

    • wisha@lemmy.ml
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      6 months ago

      If I give you the entire real line except the point at zero, what will you pick? Whatever you decide on, there will always be a number closer to zero then that.

      • sushibowl@feddit.nl
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        6 months ago

        I guess I can pick another number x to be closest to but it has the same problem unless I can guarantee it’s in the set. And successfully picking a number in the set is the problem to begin with! Foiled again!