1. The problem statement, all variables and given/known data Show that the Archimedean axiom O5 follows from the Least Upper Bound Property O6, together with the other axioms for the reals. 2. Relevant equations O5 = [if a,b > 0, then there is a positive integer n such that b<a+a+a+...+a (n summands)] or [if a,b > 0, then b < na or b/a < n] O6 = if A is any nonempty subset of R that is bounded above, then there is a least upper bound for A. 3. The attempt at a solution My teacher told us to do this as a proof by contradiction so that's the format I'll be doing. Suppose the Archimedean axiom is false towards a proof by contradiction. Therefore, there exists some a,b > 0 such that b [itex]\geq[/itex] na, or b/a [itex]\geq[/itex] n. Then the set, say N, is bounded above by b/a and so sup(N) exists. Write sup(N) = S. And then I can't figure out how to finish this proof.