## Introduction to real analysisAn elementary introduction to analysis. Limits the discussion to one variable, and presents detailed explanations and examples, focusing considerable attention on error estimation and other concepts relevant to computer science. |

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#### Review: Introduction to Real Analysis

User Review - grixor - GoodreadsThe book is very well written, logically organized and easy to read. Read full review

#### Review: Introduction to Real Analysis

User Review - Ron - GoodreadsThis book was used in my Real Analysis course. The subject would be hard to learn from this book alone, but lucky for me I had a great teacher at San Jose State University. For those trying to use the ... Read full review

### Contents

CHAPTER ONE A Glimpse at Set Theory | 1 |

CHAPTER TWO The Real Numbers | 27 |

CHAPTER THREE Sequences | 69 |

Copyright | |

7 other sections not shown

### Common terms and phrases

absolutely convergent apply approximation arbitrary Archimedean Property bounded function calculate Cauchy sequence cluster point conclude continuous function convergent sequence converges uniformly Corollary countable defined Definition denote derivative differentiable divergent elements end point establish example Exercises for Section exists a point Figure finite number follows from Theorem function g g is continuous given Hence If/is implies improper integral inequality infinite Lemma Let A C R let c e let f lim g lim xj limit mathematical induction Mean Value Theorem monotone natural number Note obtain open sets partition point c e polynomial positive real numbers Proof properties Prove rational number reader result Riemann integral satisfy sequence of real Show that lim strictly increasing strictly positive subinterval subset Suppose supremum Taylor's Theorem that/is uniform convergence uniformly continuous upper bound whence it follows