Real Analysis: Sequences and Limits

This lecture introduces the concept of real sequences, defining them as countable sets of real numbers. The instructor explains the method of proof by induction, focusing on the principle of mathematical induction. Examples of real sequences are provided, such as the Fibonacci sequence. The lecture also covers arithmetic and geometric sequences, majoring, minoring, and bounded sequences. The concept of limits of sequences is discussed, emphasizing the importance of understanding convergence and divergence. The instructor illustrates the definition of limits using epsilon-delta notation and demonstrates how to prove the existence of limits through examples and mathematical reasoning.