Sequence Convergence: Definitions and Properties

This lecture covers the definitions and properties related to sequence convergence. It starts by defining bounded sequences and then moves on to discuss increasing and decreasing sequences. The concept of a sequence tending towards a limit is explained, along with the properties of limits. The lecture also introduces the concept of convergence towards zero and explores the uniqueness of limits. The two gendarmes theorem is presented as a method to study sequences. Various examples and proofs are provided to illustrate the concepts discussed.