Least upper bound axiom: Every non-empty subset of $\mathbb R$ that has an upper bound must have a least upper bound.
This sounds too obvious as it works for both closed and open subsets of $\mathbb R$
A newcomer naive person will say:
Every subset of $\mathbb R$ must have a least upper bound
Then he realizes the first limitation that the subset of $\mathbb R$ must be non-empty.
Then after some time he realizes the second limitation that subset of $\mathbb R$ must have an upper bound.
Only then he states the least upper bound axiom completely.
No person who have gone through this axiom have found other limitations. This doesn't mean that there are no other limitations.
So how can we say that we have now stated the least upper bound axiom completely? And how can we justify its applications in several areas of mathematics (as there is a probability that the lub axiom is incomplete)?