- 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.
| Description : | Download free course An Introduction to Real Analysis, a PDF ebook by John K. Hunter. |
| Level : | Beginners |
| Created : | March 25, 2016 |
| Size : | 2.71 MB |
| File type : | |
| Pages : | 305 |
| Author : | John K. Hunter |
| Downloads: | 307 |
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