If R is the union of the nonempty left ray A and the nonempty right ray B, and A and B do not intersect, then either A has a largest element or B has a smallest element.
If A is a number set and b is a number such that if x A then x < b, then there is a number q such that if x is in A then x < q and if r < q then there is a y in A such that r < y < q.
Show that Axiom 2 if an only if Axiom 1
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