LEADER 04646oam 22006372 450 001 9910860816603321 005 20210128030655.0 010 $a1-00-310524-6 010 $a1-003-10524-6 010 $a1-000-29957-0 010 $a1-000-29963-5 024 8 $a10.1201/9781003105244 024 8 $a401950 024 8 $a9781000299632 035 $a(CKB)4100000011559710 035 $a(MiAaPQ)EBC6385092 035 $a(OCoLC)1184122111$z(OCoLC)1202870477$z(OCoLC)1206397214 035 $a(OCoLC-P)1184122111 035 $a(FlBoTFG)9781003105244 035 $a(OCoLC)1230557609 035 $a(OCoLC-P)1230557609 035 $a(CaSebORM)9781000299632 035 $a(EXLCZ)994100000011559710 100 $a20200806d2021 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aJourney from natural numbers to complex numbers /$fNita H. Shah and Thakkar D. Vishnuprasad 205 $a1st. 210 1$aBoca Raton :$cCRC Press,$d2021. 215 $a1 online resource (95 pages) $cillustrations 225 1 $aCRC focus series 225 1 $aAdvances in mathematics and engineering 300 $aIncludes index. 311 $a0-367-61333-6 311 $a0-367-61332-8 327 $aCover -- 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 327 $a1.2.8 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 327 $aChapter 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 327 $a4.5 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 330 $a"This book covers the fundamentals, proof of theorems, examples, definitions, and concepts. It explains the theory in an easy and understandable manner and offers problems for understanding and extensions of concept are included. The book provides concepts in other fields and includes an understanding of handling of numbers by computers. Research scholars and students working in the fields of engineering, science, and different branches of mathematics will find this book of interest, as it provides the subject in a clear and concise way"--$cProvided by publisher. 606 $aNumber theory 606 $aNumbers, Complex 615 0$aNumber theory. 615 0$aNumbers, Complex. 676 $a512.7 700 $aShah$b Nita H.$01730539 702 $aVishnuprasad$b Thakkar D. 801 0$bOCoLC-P 801 1$bOCoLC-P 906 $aBOOK 912 $a9910860816603321 996 $aJourney from natural numbers to complex numbers$94168046 997 $aUNINA