Convergent Sequences: Definitions and Illustrations

This lecture covers the definition of convergent sequences, with illustrations in R², and the concept of bounded sequences in IR. It also explains the definition of subsequences and the Bolzano-Weierstrass theorem. The instructor demonstrates how to identify bounded sequences and sub-sequences, and how to prove convergence in R². The lecture concludes with a discussion on the properties of compact sets and the uniqueness of limits. Various examples and proofs are provided to enhance understanding.