Demonstration of Definitions Equivalence

This lecture covers the demonstration of the equivalence of definitions for functions with limits, focusing on the concept of limits as x approaches a specific value. It explains the conditions under which a function f: D-R admits a limit L when x tends towards X. The lecture also explores the use of epsilon-delta notation to define limits rigorously and introduces the concept of sequences in the context of function continuity. The instructor illustrates the proof by contradiction method to establish the equivalence of different definitions, emphasizing the importance of precise mathematical reasoning.