3. Discovery of Real Numbers: Through Traditional Algebra

  1. Ulrich L. Rohde1,2,
  2. G. C. Jain3,
  3. Ajay K. Poddar2 and
  4. A. K. Ghosh4

Published Online: 28 DEC 2011

DOI: 10.1002/9781118130155.ch3

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

How to Cite

Rohde, U. L., Jain, G. C., Poddar, A. K. and Ghosh, A. K. (2011) Discovery of Real Numbers: Through Traditional Algebra, in Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118130155.ch3

Author Information

  1. 1

    BTU Cottbus, Germany

  2. 2

    Synergy Microwave Corporation, Paterson, NJ, USA

  3. 3

    Defense Research & Development Organization, Maharashtra, India

  4. 4

    Department of Aerospace Engineering, Indian Institute of Technology – Kanpur, Kanpur, India

Publication History

  1. Published Online: 28 DEC 2011
  2. Published Print: 9 DEC 2011

ISBN Information

Print ISBN: 9781118117750

Online ISBN: 9781118130155

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Keywords:

  • traditional algebra, discovery of real numbers;
  • real numbers and geometric constructions;
  • property of denseness, property of real numbers

Summary

This chapter contains sections titled:

  • Introduction

  • Prime and Composite Numbers

  • The Set of Rational Numbers

  • The Set of Irrational Numbers

  • The Set of Real Numbers

  • Definition of a Real Number

  • Geometrical Picture of Real Numbers

  • Algebraic Properties of Real Numbers

  • Inequalities (Order Properties in Real Numbers)

  • Intervals

  • Properties of Absolute Values

  • Neighborhood of a Point

  • Property of Denseness

  • Completeness Property of Real Numbers

  • (Modified) Definition II (l.u.b.)

  • (Modified) Definition II (g.l.b.)