I'm really sorry if this question has been asked before, I looked but couldn't find anything.
I'm going through an elementary number theory book and in the first chapter it introduces the least integer principle. There is no proof accompanied with it, it just states: "a nonempty set of integers that is bounded below contains a smallest element."
Is the reason the book doesn't give a proof because we take this as an axiom? Or is the proof so trivial that it need not be written?