I just read this whole article: http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf which is also discussed over here: Infinite sets don't exist!? However, the paragraph which I found most ...
What does Zermelo–Fraenkel set theory mean? According to Wikipedia, Zermelo–Fraenkel set theory is a set theory that is proposed to overcome issues in naive set theory. I really appreciate if ...
Other ways to put it: Is there any faith required in the adoption of a system of axioms? How is a given system of axioms accepted or rejected if not based on blind faith? (PD: I'm not religious)
I read a discussion concerning the axiom schema of specification, which I yet take as saying that for every set and a class-defining condition, those elements of the set satisfying this condition ...
Suppose the study of some kind of mathematical object has evolved in an "organic" fashion, until it reaches the level of maturity that one wants to take an axiomatic approach to the study of those ...
Or alternative you need to assume CH is false. I know several proofs that use axiom of choice. Heine Borel theorem is the best example I can think off. Zorns lemma is heavily used in the non ...