Real Numbers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Real Numbers write by Jean E. Cunningham. This book was released on 2017-09-30. Real Numbers available in PDF, EPUB and Kindle. How management accounting evolved with Lean principles.
The Real Numbers and Real Analysis
The Real Numbers and Real Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Real Numbers and Real Analysis write by Ethan D. Bloch. This book was released on 2011-05-27. The Real Numbers and Real Analysis available in PDF, EPUB and Kindle. 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.
The Real Numbers
The Real Numbers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Real Numbers write by John Stillwell. This book was released on 2013-10-16. The Real Numbers available in PDF, EPUB and Kindle. 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.
Which Numbers Are Real?
Which Numbers Are Real? - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Which Numbers Are Real? write by Michael Henle. This book was released on 2012-12-31. Which Numbers Are Real? available in PDF, EPUB and Kindle. 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.
The Real Number System
The Real Number System - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Real Number System write by John M. H. Olmsted. This book was released on 2018-09-12. The Real Number System available in PDF, EPUB and Kindle. Concise but thorough and systematic, this categorical discussion presents a series of step-by-step axioms. The highly accessible text includes numerous examples and more than 300 exercises, all with answers. 1962 edition.
