Tagged Questions
22
votes
7answers
1k views
Does mathematics require axioms?
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 ...
2
votes
1answer
141 views
Explain Zermelo–Fraenkel set theory in layman terms
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 ...
20
votes
5answers
715 views
How is a system of axioms different from a system of beliefs?
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)
-3
votes
4answers
208 views
What are some primary mathematical utilities of the axiom schema of separation?
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 ...
2
votes
1answer
66 views
How does one formulate a minimal set of axioms? [closed]
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 ...
12
votes
1answer
524 views
Proofs given in undergrad degree that need Continuum hypothesis?
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 ...
