Dedekind Cuts: Rational Numbers

This lecture covers the concept of Dedekind cuts in the context of rational numbers, exploring the properties and relationships between different cuts, as well as their applications in defining real numbers. The instructor explains how Dedekind cuts can be used to construct the real number system from rational numbers, emphasizing the importance of these cuts in establishing a complete and ordered field. Various examples and definitions are provided to illustrate the concept of Dedekind cuts and their role in the development of real analysis.