Preface Chapter 1.Natural Numbers 1.1.Peano Systems 1.2.Addition 1.3.Multiplication 1.4.Order 1.5.Isomorphism of Peano Systems 1.6.A Set-Theoretic Model 1.7.Recursion 1.8.Mathematical Induction 1.9.Algebraic Structures Notes Exercises Chapter 2.Integers 2.1.Definition of the Integers 2.2.Addition of Integers 2.3.Multiplication of Integers 2.4.Order 2.5.Rings and Integral Domains Notes Exercises Chapter 3.Rational Numbers 3.1.Definition of Rational Numbers 3.2.Addition of Rational Numbers 3.3.Multiplication of Rational Numbers 3.4.Order 3.5.Algebraic Structures on Q 3.6.Convergence in an Ordered Field 3.7.Limitations of Q Notes Exercises Chapter 4.Real Numbers 4.1.Definition of Real Numbers 4.2.Operations on R 4.3.R as a Field 4.4.R as an Ordered Field 4.5.Cauchy Completeness of R 4.6.Dedekind Completeness of R 4.7.Continuous Functions on R Notes Exercises Chapter 5.Complex Numbers 5.1.Definition of Complex Numbers 5.2.The Field C of Complex Numbers 5.3.C as a Vector Space 5.4.C as a Normed Algebra 5.5.Convergence in C 5.6.Roots of Complex Numbers 5.7.Continuous functions 5.8.The Fundamental Theorem of Algebra
Notes Exercises Appendix A.Sets, Relations, Functions A.I.Sets A.2.Operations on Sets A.3.Relations A.4.Functions and Operations Notes Exercises Bibliography Index
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