Quote by Oxymoron
For example. Suppose I choose my favourite nonempty, wellordered set, X. Then I would not be able to define an explicit choice function for this set. However if I choose my favourite nonempty set, X, such that every element is a wellordered set, then I would be able to define an explicit choice function because I could let my function choose the least element of each set of X. Is this correct reasoning?

At first glance, that looks good. But what is a wellordered set? It is a set that has a wellorder. But in general, a wellordered set has many wellorders. So for each set you can't first just say "pick the least element" you first have to pick a wellorder, then you can choose the least element. But the problem of picking a wellorder for each set is tricky in itself. I have to think on how you'd do this.