Limit Superior and Limit Inferior

This lecture covers the concepts of limsup and liminf, illustrated with an exam-type exercise and examples. It explains the Bolzano-Weierstrass theorem, accumulation points, and the properties of bounded sequences. The lecture also delves into the concepts of lower and upper limits, convergence of subsequences, and the convergence of bounded sequences. The instructor demonstrates the calculation of limsup and liminf for various sequences, emphasizing the importance of accumulation points and the convergence of bounded sequences.