Irrational Numbers and Their Representation by Sequences and Series
by Henry Parker Manning
Publisher: J. Wiley & sons 1906
Number of pages: 156
This book is intended to explain the nature of irrational numbers, and those parts of Algebra which depend on what is usually called The Theory of Limits. We have endeavored to show how the fundamental operations are to be performed in the case of irrational numbers and to define the irrational exponent and the logarithm.
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by B. Lafferriere, G. Lafferriere, N. Mau Nam - Portland State University Library
We provide students with a strong foundation in mathematical analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
by Larry Clifton - arXiv
This is a detailed introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios, and then define the positive real numbers categorically.
by W W L Chen - Macquarie University
An introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory. Contents: the real numbers and countability, the Riemann integral, point sets, the Lebesgue integral, monotone convergence theorem, etc.
by Robert Rogers, Eugene Boman - Open SUNY Textbooks
This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. The book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments.