Real Functions: Definitions and Limits

This lecture covers real functions of several real variables, including definitions and results related to functions defined on subsets of R^n. It explores concepts such as bounded functions, limits at a point, and generalizations from single-variable functions. The instructor explains the importance of understanding functions in multiple dimensions and clarifies ambiguities that may arise when dealing with sequences in R^n. The lecture concludes with a theorem stating the uniqueness of limits for functions defined on subsets of R^n. Overall, the lecture provides a comprehensive overview of real functions and their properties.