Why is the axiom of choice an axiom?

Related questions

1. What is an ordering principle in English?
2. What is corollary math?
3. Can an element be a set?
4. What is an example of a corollary?
5. Is Zfc consistent?
6. How do you prove well ordering principle?
7. Can postulates be used in proofs?
8. Can a set contain itself?
9. What does axiom of choice mean?
10. What does it mean for a set to be well ordered?

Tags

1. #axiom
2. #sometimes
3. #mutually
4. #important
5. #common
6. #disjoint
7. #least
8. #formulated
9. #there
10. #exists
11. #contains
12. #exactly
13. #choice
14. #zermelo
15. #states
16. #given
17. #called
18. #theory
19. #element
20. #nonempty
21. #fundamental