## An Introduction to AnalysisOffering readability, practicality and flexibility, Wade presents Fundamental Theorems from a practical viewpoint. Introduces central ideas of analysis in a one-dimensional setting, then covers multidimensional theory. Offers separate coverage of topology and analysis. Numbers theorems, definitions and remarks consecutively. Uniform writing style and notation. Practical focus on analysis. For those interested in learning more about analysis. |

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8 pages matching **rational numbers** in this book

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### Contents

ONEDIMENSIONAL THEORY | 1 |

Sequences in R | 35 |

Continuity on R | 58 |

Copyright | |

18 other sections not shown

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algebraic bounded interval bounded variation Br(a Br(x Cauchy choose closed interval connected contains continuous functions continuously differentiable contradiction converges absolutely converges uniformly convex cosx countable curve defined definition diverges E C R Example Exercise exists extended real number f is continuous f(xo fc=i fc=l Figure finite following result shows formula graph Hence holds hypothesis implies xn improper integral improperly integrable inequality infimum integrable on 0,1 Intermediate Value Theorem Jordan region l,oo Lemma Mean Value Theorem metric space monotone nonempty subset nonnegative nonzero notation Notice open ball open interval open sets parametrization partial sums partition pointwise power series Proof Property Prove radius of convergence real functions real sequence rectangle relatively open Remark Riemann integral satisfies sinx smooth Squeeze Theorem Suppose that xn supremum surface tangent uniformly continuous variables vector YlT=i zero