Subsequences and Bolzano-Weierstrass Theorem

This lecture covers the squeeze theorem for unbounded sequences, limits of monotone sequences, definitions and properties of subsequences, and the Bolzano-Weierstrass theorem. It explains the concept of monotone sequences, the importance of boundedness, and the existence of limits for certain sequences. The lecture also delves into the construction of monotone subsequences and the significance of peaks in sequences, discussing the conditions for a peak and the behavior of peaks in sequences. Additionally, it explores the implications of the Bolzano-Weierstrass theorem in identifying convergent subsequences and the role of peaks in determining the convergence of sequences.