[lheck]

> Is this only a problem for infinite sets (of sets to pick from)?

I've edited this a lot, but it might still depend on the AoC if you can construct such a function in general, my ideas didn't work (e.g. two complex infinite sets per set are already hard)

> Is it trivial to construct a function that picks a single element from an arbitrary set that’s not ordered numbers (say, the real endomorphisms)?

With no constraints on the function this is the AoC.