More On Closed Sets

We show that limit points are the limits of sequences, which shows that closed sets contain the limit points of their sequences. We also explain that open and closed sets are complementary, allowing us to prove analogues for closed sets of the arbitrary union and finite intersection theorems for open sets. 0:00, Intro 0:22, Theorem (Limit points of sets are limit points of sequences) 2:54, Forward proof of Theorem (Limit points of sets are limit points of sequences) 8:30, Backward proof of Theorem (Limit points of sets are limit points of sequences) 13:57, Theorem (Closed is equivalent to containing the limits of Cauchy Sequences) 15:13, Example of Theorem (Closed is equivalent to containing the limits of Cauchy Sequences) 16:29, Theorem (Open sets and Closed sets are Complementary) 17:53, Theorem (Closed sets are preserved by Finite Unions and Any Intersections) 19:00, Proof of Theorem (Closed sets are preserved by Finite Unions and Any Intersections) 22:05, Tease about new Ideas