Real Numbers: Properties and Formulas

This lecture covers the introduction to real numbers, including the concept of supremum, infimum, maximum, and minimum. It also delves into the fundamental properties of real numbers, such as the existence of a maximum and minimum for any non-empty set in the real numbers. The lecture further explores the definitions and examples of minorants and majorants, emphasizing the distinction between the real numbers and rational numbers. The concept of infimum is highlighted, showcasing its significance in determining the greatest lower bound of a set. Various formulas and properties related to real numbers are discussed, providing a comprehensive understanding of this fundamental mathematical concept.