Journey from natural numbers to complex numbers /
Shah, Nita H.,
Journey from natural numbers to complex numbers / Nita H. Shah and Thakkar D. Vishnuprasad. - 1 online resource. - CRC focus series Advances in mathematics and engineering .
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
"This book covers the fundamentals, proof of theorems, examples, definitions, and concepts. It explains the theory in an easy and understandable manner and offers problems for understanding and extensions of concept are included. The book provides concepts in other fields and includes an understanding of handling of numbers by computers. Research scholars and students working in the fields of engineering, science, and different branches of mathematics will find this book of interest, as it provides the subject in a clear and concise way"--
9781003105244 1003105246 9781000299632 1000299635 9781000299571 1000299570 9781000299601 1000299600
Numbers, Natural.
Numbers, Complex.
MATHEMATICS / Applied
TECHNOLOGY / Operations Research
BUSINESS & ECONOMICS / Operations Research
QA141
512.7
Journey from natural numbers to complex numbers / Nita H. Shah and Thakkar D. Vishnuprasad. - 1 online resource. - CRC focus series Advances in mathematics and engineering .
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
"This book covers the fundamentals, proof of theorems, examples, definitions, and concepts. It explains the theory in an easy and understandable manner and offers problems for understanding and extensions of concept are included. The book provides concepts in other fields and includes an understanding of handling of numbers by computers. Research scholars and students working in the fields of engineering, science, and different branches of mathematics will find this book of interest, as it provides the subject in a clear and concise way"--
9781003105244 1003105246 9781000299632 1000299635 9781000299571 1000299570 9781000299601 1000299600
Numbers, Natural.
Numbers, Complex.
MATHEMATICS / Applied
TECHNOLOGY / Operations Research
BUSINESS & ECONOMICS / Operations Research
QA141
512.7