Real Numbers: Decimal Notation

This lecture introduces the concept of real numbers, focusing on decimal notation and the transition from integers to fractions. The instructor explains the complexity of constructing real numbers and provides insights into the challenges of studying decimal numbers rigorously. Through examples, students learn how to represent decimal numbers as fractions and simplify calculations. The lecture also covers the notation of decimal numbers, emphasizing the relationship between decimal digits and powers of 10. By the end, students gain a solid understanding of how to express decimal numbers as fractions and the importance of simplification in calculations.