Supremum of the Union of Sets | Real Analysis

If A and B are two bounded and nonempty subsets of the real numbers, then what is the supremum of their union? What is supAUB? Well, if A and B are bounded nonempty subsets of the reals then we know they both have supremums by the completeness axiom. Then, as it turns out, the supremum of AUB is actually the supremum of { supA, supB }. In other words, the supremum of AUB is just the bigger of sup A and sup B. We'll go over a proof of this result in today's real analysis lesson!

Definition of supremum and infimum: Definition of Supremum and Infimum of...
Proof that the maximum of a set is the supremum: Proof: Maximum of a Set is the Suprem...

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