Real Analysis and Infinity [Hardcover]

Real Analysis and Infinitypresents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts.Real Analysis and Infinitypresents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts. After introducing sequences of numbers, it develops the set of real numbers in terms of Cauchy sequences of rational numbers, and uses this development to derive the important properties of real numbers like completeness. The book then develops the concepts of continuity, derivative, and integral, and presents the theory of infinite sequences and series of functions.Topics discussed are wide-ranging and include the convergence of sequences, definition of limits and continuity via converging sequences, and the development of derivative. The proofs of the vast majority of theorems are presented and pedagogical considerations are given priority to help cement the reader's knowledge.Preliminary discussion of each major topic is supplemented with examples and diagrams, and historical asides. Examples follow most major results to improve comprehension, and exercises at the end of each chapter help with the refinement of proof and calculation skills.Preface1. Manifestations of Infinity: An Overview2. Sets, Functions, Logic and Countability3. Sequences and Limits4. The Real Numbers5. Infinite Series of Constants6. Differentiation and Continuity7. Integration8. Infinite Sequences and Series of FunctionsAppendix: Cantor's Construction: Additional DetailAppendix: Discontinuity in a Space of FunctionsReferences and Further ReadingHassan Sedaghat,Professor Emeritus of Mathematics, Virginia Commonwealth University, USAHassan Sedaghatis Professor Emeritus of Mathematics at Virginia Commonwealth University, USA. He has over 35 years of teaching experience in college mathematics, from freshman to the postgradl£Ø