Real Number Sequences

This lecture covers the basics of real number sequences, defining them as infinite families of numbers indexed by integers. It explains the concepts of increasing and decreasing sequences, as well as bounded and convergent sequences. The lecture also introduces the notion of limits and convergence, illustrating the properties of monotonic and bounded sequences. The 'Two Policemen Theorem' is presented as a method to study sequences using upper and lower bounds. Various examples are provided to demonstrate the convergence and properties of sequences.