Hetware wrote: > On 10/7/2013 9:36 AM, Peter Percival wrote: >> Hetware wrote: >>>> >>> >>> It does me no good to simply accept what someone tells me without being >>> able to derive it in some sense from first principles. >> >> Good luck with that. What are those first principles? Is it set >> theory? If so, are the axiom what someone else tells us they are? If >> no, what? >> > > They are the axioms I assume, and hopefully those others agree upon. But > that is often far from clear upon careful examination.
If you're a student, it's best to "assume" the axioms that your instructors "assume", else you'll fail the exams. So far as set theory is concerned there are two commonly used theories of sets and a small number of others, if you take a course in set theory and the instructor is teaching (let's say) Zermelo-Fraenkel it would be daft of you to "assume" Kelly-Morse. That would be as silly as taking a course on group theory and "assuming", instead of the axioms for groups, those for Moufang loops.
-- The world will little note, nor long remember what we say here Lincoln at Gettysburg