Journey from Natural Numbers to Complex Numbers

Journey from Natural Numbers to Complex Numbers

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Bibliographic Details
Main Author: Shah, Nita H.
Other Authors: Thakkar, Vishnuprasad D.
Format: eBook
Language:English
Published: Milton : Taylor & Francis Group, 2020.
Series:Advances in Mathematics and Engineering Ser.
Subjects:
Numbers, Natural.
Numbers, Complex.
Online Access:Click for online access
Table of Contents:
  • Cover
  • Half Title
  • Series Page
  • Title Page
  • Copyright Page
  • Table of Contents
  • Preface
  • Author biographies
  • Chapter 1 Natural Numbers
  • 1.1 Prerequisites
  • 1.1.1 Set Theory
  • 1.1.2 Relation
  • 1.1.3 Function
  • 1.1.4 Cardinality
  • 1.1.5 Algebra
  • 1.2 Positive Integers
  • 1.2.1 Positive Integers in Real Life
  • 1.2.2 Set Theoretic Definition of Natural Numbers
  • 1.2.3 Peano Axioms
  • 1.2.4 Ordering in Natural Numbers
  • 1.2.5 First Principle of Mathematical Induction
  • 1.2.6 Second Principle of Mathematical Induction
  • 1.2.7 Well-Ordering Principle
  • 1.2.8 Limitations of Natural Numbers
  • 1.2.9 Representation of Natural Numbers
  • 1.2.9.1 Hexadecimal System
  • 1.2.10 Number System Used by Computers
  • 1.3 Summary
  • Chapter 2 Integers
  • 2.1 Informal Introduction of Integers
  • 2.2 Integers as Relation in Ordered Pairs of Natural Numbers
  • 2.3 Ordering in Ordered Pairs
  • 2.4 Operations in Ordered Pairs of Natural Numbers
  • 2.5 Properties of Binary Operations
  • 2.6 Interpretation of Relation and Operations
  • 2.7 Mapping of Ordered Pairs as Extension of Natural Numbers
  • 2.8 Representation of Integers
  • 2.9 Summary
  • Chapter 3 Rational Numbers
  • 3.1 Informal Introduction of Rational Numbers
  • 3.2 Rational Numbers as Relation in Ordered Pairs of Integers
  • 3.3 Ordering in Ordered Pairs
  • 3.4 Operations in Ordered Pairs
  • 3.5 Properties of Binary Operations
  • 3.6 Interpretation of Relation and Operations
  • 3.7 Mapping of Ordered Pairs as Extension of Integers
  • 3.8 Representation of Rational Numbers
  • 3.9 Limitations of Rational Numbers
  • 3.10 Summary
  • Chapter 4 Real Numbers
  • 4.1 Least Upper Bound Property
  • 4.2 Rational Cuts
  • 4.3 Dedekind Cuts
  • 4.4 Ordering in Cuts
  • 4.5 Binary Operations in Cuts
  • 4.6 Least Upper Bound Property
  • 4.7 Set of Cuts as Extension of Rational Numbers
  • 4.8 Cardinality of Set of Real Numbers
  • 4.9 Limitations of Real Numbers
  • 4.10 Summary
  • Chapter 5 Complex Numbers
  • 5.1 Complex Numbers as Ordered Pairs of Real Numbers
  • 5.2 Binary Operations in Complex Numbers
  • 5.3 Introduction of Imaginary Numbers
  • 5.4 Representation of Complex Numbers
  • 5.5 Ordering in Complex numbers
  • 5.6 Cardinality of the Set of Complex Numbers
  • 5.7 Algebraic Numbers
  • 5.8 Summary
  • Index

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