[PDF] An Introduction to Real Analysis Learn Math Course

Chapter 1. Sets and Functions
Chapter 2. Numbers
Chapter 3. Sequences
Chapter 4. Series
Chapter 5. Topology of the Real Numbers
Chapter 6. Limits of Functions
Chapter 7. Continuous Functions
Chapter 8. Differentiable Functions
Chapter 9. Sequences and Series of Functions
Chapter 10. Power Series
Chapter 11. The Riemann Integral
Chapter 12. Properties and Applications of the Integral
Chapter 13. Metric, Normed, and Topological Spaces

Learning the An Introduction to Real Analysis

Leopold Kronecker believed that God was the one who devised the integers, while man was responsible for everything else in the world. The real numbers are a group of things that are referred to as the elements or members of the set. Both of these terms refer to the individuals that make up the set. They could be anything—planets, characters in Shakespeare's plays, or even squirrels—but for our purposes, they will be mathematical objects or sets of numbers. They could even be squirrels. In this chapter, we will talk about the qualities that are present across all of the fundamental number systems. After a cursory review of the integers and rational numbers to get our bearings, we move on to the real numbers and conduct a more in-depth investigation of them.

The real numbers collectively make up the entire number system that is referred to as the real numbers. The rational numbers are a compact subset of the real numbers. The fact that the representation of real numbers is more comprehensive than that of rational numbers distinguishes them from the latter.