The Real Number System

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The Real Number System

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Author : John M. H. Olmsted
language : en
Publisher: Courier Dover Publications
Release Date : 2018-09-12

The Real Number System written by John M. H. Olmsted and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-12 with Mathematics categories.

Concise but thorough and systematic, this categorical discussion of the real number system presents a series of step-by-step axioms, each illustrated by examples. The highly accessible text is suitable for readers at varying levels of knowledge and experience: advanced high school students and college undergraduates as well as prospective high school and college instructors. The abundance of examples and the wealth of exercises—more than 300, all with answers provided—make this a particularly valuable book for self-study. The first two chapters examine fields and ordered fields, followed by an introduction to natural numbers and mathematical induction. Subsequent chapters explore composite and prime numbers, integers and rational numbers, congruences and finite fields, and polynomials and rational functions. Additional topics include intervals and absolute value, the axiom of completeness, roots and rational exponents, exponents and logarithms, and decimal expansions. A helpful Appendix concludes the text.

The Number System

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Author : H. A. Thurston
language : en
Publisher: Courier Corporation
Release Date : 2012-10-23

The Number System written by H. A. Thurston and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-23 with Mathematics categories.

This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.

The Structure Of The Real Number System

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Author : Leon Warren Cohen
language : en
Publisher:
Release Date : 2012-07-01

The Structure Of The Real Number System written by Leon Warren Cohen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-01 with categories.

Additional Editor Is Paul R. Halmos. The University Series In Undergraduate Mathematics.

Which Numbers Are Real

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Author : Michael Henle
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-12-31

Which Numbers Are Real written by Michael Henle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Mathematics categories.

Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics. Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book. Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.

Labyrinth Of Thought

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Author : Jose Ferreiros
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-01

Labyrinth Of Thought written by Jose Ferreiros and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-01 with Mathematics categories.

"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

Number Systems And The Foundations Of Analysis

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Author : Elliott Mendelson
language : en
Publisher: Dover Books on Mathematics
Release Date : 2008

Number Systems And The Foundations Of Analysis written by Elliott Mendelson and has been published by Dover Books on Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.

The Real Numbers

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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-16

The Real Numbers written by John Stillwell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-16 with Mathematics categories.

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

The Real Numbers And Real Analysis

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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27

The Real Numbers And Real Analysis written by Ethan D. Bloch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-27 with Mathematics categories.

This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.

College Algebra

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Author : OpenStax
language : en
Publisher:
Release Date : 2016-10-11

College Algebra written by OpenStax and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-11 with Mathematics categories.

College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. The text and images in this textbook are grayscale.

The Real Number System In An Algebraic Setting

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Author : J. B. Roberts
language : en
Publisher: Courier Dover Publications
Release Date : 2018-04-18

The Real Number System In An Algebraic Setting written by J. B. Roberts and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-18 with Mathematics categories.

Originally published: San Francisco: W.H. Freeman, 1962.