Let A, B be nonempty subsets of ?, let B be bounded, and suppose that A ? B. Prove that sup A ? sup B.
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Now, since B is bounded, there exists an upper bound for B. Let's call this upper bound M. Since A is a subset of B, M is also an upper bound for A. Now, let's consider the least upper bounds (suprema) of A and B. By definition, sup A is the smallest upper bound Show more…
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