04646oam 22006372 450 991086081660332120210128030655.01-00-310524-61-003-10524-61-000-29957-01-000-29963-510.1201/97810031052444019509781000299632(CKB)4100000011559710(MiAaPQ)EBC6385092(OCoLC)1184122111(OCoLC)1202870477(OCoLC)1206397214(OCoLC-P)1184122111(FlBoTFG)9781003105244(OCoLC)1230557609(OCoLC-P)1230557609(CaSebORM)9781000299632(EXLCZ)99410000001155971020200806d2021 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierJourney from natural numbers to complex numbers /Nita H. Shah and Thakkar D. Vishnuprasad1st.Boca Raton :CRC Press,2021.1 online resource (95 pages) illustrationsCRC focus seriesAdvances in mathematics and engineeringIncludes index.0-367-61333-6 0-367-61332-8 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 Principle1.2.8 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 SummaryChapter 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 Cuts4.5 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"--Provided by publisher.Number theoryNumbers, ComplexNumber theory.Numbers, Complex.512.7Shah Nita H.1730539Vishnuprasad Thakkar D.OCoLC-POCoLC-PBOOK9910860816603321Journey from natural numbers to complex numbers4168046UNINA