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Feb 5, 2010 · SECTION 1.3 introduces basic ideas of set theory in the context of sets of real num-bers. In this section we prove two fundamental theorems: the Heine–Borel and Bolzano– Weierstrass theorems. 1.1 THE REAL NUMBER SYSTEM Having taken calculus, you know a lot about the real number system; however, you prob-
Abstract. These are some notes on introductory real analysis. They cover the properties of the real numbers, sequences and series of real numbers, limits of functions, continuity, differentiability, sequences and series of functions, and Riemann integration. They don’t include multi-variable calculus or contain any problem sets.
ISBN: 9781718862401. [JL] = Basic Analysis: Introduction to Real Analysis (Vol. 1) (PDF - 2.2MB) by Jiří Lebl, June 2021 (used with permission) This book is available as a free PDF download. You can purchase a paper copy by following a link at the same site.
The foundations of real analysis are given by set theory, and the notion of cardinality in set theory, as well as the axiom of choice, occur frequently in analysis.
also include some additional material on real powers and the exponential function. I recommend you refer to these notes for learning the mathematical content of the course, and refer to the textbook for examples, pictures, and additional exercises.
Abstract. These are some notes on introductory real analysis. They cover limits of functions, continuity, differentiability, and sequences and series of functions, but not Riemann integration A background in sequences and series of real numbers and some elementary point set topology of the real numbers
Real Analysis. A Comprehensive Course in Analysis, Part 1. Barry Simon. Providence, Rhode Island. 2010 Mathematics Subject Classification. Primary 26-01, 28-01, 42-01, 46-01; Secondary 33-01, 35-01, 41-01, 52-01, 54-01, 60-01. For additional information and updates on this book, visit. www.ams.org/bookpages/simon.
