Open and Closed Sets

This lecture covers the concepts of open and closed sets in the context of real numbers. It explains that a set is open if, for every element in the set, there exists an open interval around that element entirely contained in the set. It also discusses closed sets, providing examples and demonstrating how to determine if a set is open or closed. The lecture concludes by highlighting the importance of defining sets as either open or closed to ensure coherence in mathematical analysis.