In my abstract algebra book one of the first facts stated is the Well Ordering Principle:
(*) Every non-empty set of positive integers has a smallest member.
In real analysis on the other hand one of the first things introduced are the real numbers and their Completeness Axiom:
Every nonempty set of real numbers having an upper bound must have a least upper bound.
Which is equivalent to:
(**) Every nonempty set of real numbers having a lower bound must have a biggest lower bound (infimum).
It has never been mentioned in any book I've read and I don't know if they have anything to do with each other but (*) and (**) seem to me to be such that (**) implies (*).
Is the Well Ordering Principle a consequence of the Completeness of the real numbers? Or do they have nothing to do with each other? How should I think of them in terms of how they relate to each other?
Is it okay to see one as a consequence of the other?