We introduce coverings of sets, finite subcovers, and compact sets in the context of real analysis. These concepts will be critical in our continuing discussion of the topology of the reals. The definition of a compact set, in particular, is surprisingly fundamental, and we will provide and prove equivalent definitions of compactness in other videos. For now, we say a set A is compact if every open cover of the set A contains a finite subcover. #realanalysis

Open Sets:    • Intro to Open Sets (with Examples) | ...  
Closed Sets:    • All About Closed Sets and Closures of...  
Identifying Open, Closed, and Compact Sets:    • Identifying Open, Closed, and Compact...  
All About Compact Sets: (coming soon)

Real Analysis Course:    • Real Analysis  
Real Analysis exercises:    • Real Analysis Exercises  

◉Textbooks I Like◉
Graph Theory: https://amzn.to/3JHQtZj
Real Analysis: https://amzn.to/3CMdgjI
Proofs and Set Theory: https://amzn.to/367VBXP (available for free online)
Statistics: https://amzn.to/3tsaEER
Abstract Algebra: https://amzn.to/3IjoZaO
Discrete Math: https://amzn.to/3qfhoUn
Number Theory: https://amzn.to/3JqpOQd

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