Advanced Calculus I, Part 12, Every Sequence has a Convergent Subsequence, The Sequential Compactnes

This is the twelfth of a series of videos dealing with single variable calculus topics. We prove every sequence has a monotone subsequence. We use that to prove the Sequential Compactness Theorem that states every interval of the form [a, b] is compact.

01:45 Every sequence has a monotone subsequence.
12:42 Every bounded sequence has a convergent subsequence.
15:25 Examples of sets that are not compact.
21:26 Sequential Compactness Theorem.