Definition talk:Choice Function

So, we have an extensive rewrite of this page in some more-or-less significant ways from an anonymous editor who has not contributed anything before, and I need advice as to whether the changes are a) necessary (i.e. they fix stuff that's wrong), b) acceptable (they don't change the quality of the page either way but are just another way of stating the same thing) or c) detrimental.

The points are as follows:

1. Changing the definition of CF from a defintion as $\forall S \in \mathbb S: \exists x \in S: f \left({S}\right) = x$ to a "description" as $\forall S \in \mathbb S: f \left({S}\right) \in S$
2. Changing from AoC to AC (which may or may not be necessary) and would need to be propagated through the whole site (maybe say "AoC or AC" or something)
3. Removal of the fact that the codomain of the CF is $\bigcup \Bbb S$.
4. Statement that CF is now "generally accepted", and removal of the discussion about its non-acceptance. (What I would have liked this site to do was to include all the different definitions and philosophical points of view rather than just reporting on one.)
5. General rewording and restructuring which I'm unconvinced about.
6. Addition of a couple of paragraphs which (for all that the editor claims to have "fixed unclarities") lack coherence and focus.

I accept that the edits are in good faith, but I'm uncertain about whether the dogmatism exhibited is justified.

Anyone out there able / willing to comment? --prime mover 01:38, 2 November 2011 (CDT)