## Analysis: with an introduction to proofCarefully focused on reading and writing proofs, this introduction to the analysis of functions of a single real variable helps readers in the transition from computationally oriented to abstract mathematics. It features clear expositions and examples, helpful practice problems, many drawings that illustrate key ideas, and hints/answers for selected problems. Logic and Proof. Sets and Functions. The Real Numbers. Sequences. Limits and Continuity. Differentiation. Integration. Infinite Series. Sequences and Series of Functions. For anyone interested in Real Analysis or Advanced Calculus. |

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#### Review: Analysis: With an Introduction to Proof

User Review - Daniel Babiak - GoodreadsStart here, then go to Rudin. Read full review

#### Review: Analysis: With an Introduction to Proof

User Review - Gloria - GoodreadsFirst edition is full of errors. Fourth still has few but it contains much more material than the first and has an improved format. It's the book you'd wish you could have read before high school ... Read full review

### Contents

Sets and Functions | 31 |

The Real Numbers | 87 |

Ordered Fields | 95 |

Copyright | |

22 other sections not shown

### Common terms and phrases

accumulation point ANSWERS TO PRACTICE apply Archimedean property axiom of choice bijection cardinal number Cauchy sequence closed sets conclude consider continuous function contradiction convergent sequence converges uniformly Corollary countable DEFINITION Let denote denumerable derivative differentiable diverges element equinumerous equivalence class equivalence relation EXAMPLE Let Exercise exists a neighborhood exists a number exists a point Figure formula function defined given implies induction injective interval of convergence Justify each answer Let f(x lim sup Mark each statement mathematical mean value theorem metric space natural numbers nonempty subset obtain open cover open set ordered field ordered pairs partial sums partition positive number power series PRACTICE PROBLEMS properties radius of convergence rational numbers real number Section series converges statement True subsequential limits surjective Taylor's theorem THEOREM Let True or False unbounded uniform convergence uniformly continuous upper bound write