1. Real Numbers and Limits of Sequences

  1. Leonard F. Richardson

Published Online: 15 FEB 2011

DOI: 10.1002/9781118032411.ch1

Advanced Calculus: An Introduction to Linear Analysis

Advanced Calculus: An Introduction to Linear Analysis

How to Cite

Richardson, L. F. (2008) Real Numbers and Limits of Sequences, in Advanced Calculus: An Introduction to Linear Analysis, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032411.ch1

Publication History

  1. Published Online: 15 FEB 2011
  2. Published Print: 11 APR 2008

ISBN Information

Print ISBN: 9781118030677

Online ISBN: 9781118032411

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Keywords:

  • real numbers;
  • limits of sequences;
  • Cauchy sequences;
  • axiom;
  • algebraic combinations

Summary

This chapter contains sections titled:

  • The Real Number System

  • Limits of Sequences & Cauchy Sequences

  • The Completeness Axiom and Some Consequences

  • Algebraic Combinations of Sequences

  • The Bolzano-Weierstrass Theorem

  • The Nested Intervals Theorem

  • The Heine-Borel Covering Theorem

  • Countability of the Rational Numbers

  • Test Yourself