1: The Real Numbers
- Page ID
- 33435
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IN THIS CHAPTER we begin the study of the real number system. The concepts discussed here will be used throughout the book.
- SECTION 1.1 deals with the axioms that define the real numbers, definitions based on them, and some basic properties that follow from them.
- SECTION 1.2 emphasizes the principle of mathematical induction.
- SECTION 1.3 introduces basic ideas of set theory in the context of sets of real numbers. In this section we prove two fundamental theorems: the Heine–Borel and Bolzano–Weierstrass theorems.