Real Numbers: Structure and Properties

This lecture covers the structure and properties of real numbers, including the introduction to the axiomatic system of real numbers, the relationship between real numbers and rational numbers, and the implications of Archimedean property. It also discusses the existence of real numbers as a model for rational numbers, the concept of irrational numbers, and the properties of real numbers. The lecture concludes with the demonstration of the existence of real numbers as a model for rational numbers.