Compact Sets Contain Supremum and Infimum | Real Analysis Exercises

We prove another nice property of compact sets. If K is a compact set, then not only do the supremum of K and the infimum of K both exist, but also they are elements of K. This is straightforward to prove since we know a compact set is closed and bounded - and a bounded set has a supremum and infimum by the axiom of completeness, and also sequences in the set converging to the sup and inf. Thus, by closure, the set must contain the sup and inf. #realanalysis

Open Sets:    • Intro to Open Sets (with Examples) | ...  
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Open Covers, Finite Subcovers, and Compact Sets:    • Open Covers, Finite Subcovers, and Co...  
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