User:IssaRice/Schröder–Bernstein theorem

questions:

• are the ancestor proof and the iterated partition proof actually different, or do they just look different on the surface?
• what is the proof that uses axiom of choice, and how does choice simplify the proof?
• is the result a fixed point result? (if so how can we phrase it as such?) or is it just that some of the proofs makes use of the fixed point ideas?