According to Theorem 3.7.2 as a given below: Theorem 3.7.2 The least upper bound principle Let S CR,S # &. We have e if S is bounded above then sup S exists, e if is bounded below then inf exists. Taking Theorem 3.7.2 as a given, we will now prove the Archimedean Property: If z R, then there exists n N such that z n. What would Theorem 3.7.2 now tell you? 3.2 Continuing by contradiction, let u = sup(N). Why must there be some m N such that