I once had a homework assignment to attempt to construct the choice function for the set made up of all non-empty subsets of the reals. A lot of intuitive ideas

I once had a homework assignment to attempt to construct the choice function for the set made up of all non-empty subsets of the reals. A lot of intuitive ideas come to mind and it's a good exercise to show why they don't work. You should feel weird about the axiom of choice after working through a few.