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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User Review  grixor  GoodreadsThe book is very well written, logically organized and easy to read. Read full review
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Contents
CHAPTER ONE A Glimpse at Set Theory  1 
CHAPTER TWO The Real Numbers  27 
CHAPTER THREE Sequences  69 
Copyright  
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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