Real Numbers: Definitions and Properties

This lecture covers the definitions and properties of real numbers, focusing on the concepts of lower and upper bounds, supremum, and infimum. The instructor explains the equivalence between these concepts and demonstrates the Archimedean property. Through examples, the lecture illustrates how to find supremum and infimum for different sets, including bounded intervals and irrational numbers. The proof techniques involve using epsilon arguments and applying the Archimedean property. The lecture concludes with a discussion on terminology, highlighting the distinction between minimum and maximum in sets of real numbers.