Hi, I was wondering if I correctly applied the properties of the supremum of a set to solve the following proof. I feel like I "cheated" in the sense that I said, "Let s = Sup(B) - epsilon.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

If [itex]\sup A < \sup B[/itex], then show that there exists an element [itex]b \in B[/itex] that is an upper bound for [itex]\sup A[/itex].

2. Relevant equations

None

3. The attempt at a solution

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# Homework Help: Am I correctly using the properties of the supremum in this proof?

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