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Description
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Dr. Bridger chooses families of rational intervals, rather than Cauchy sequences, to define real numbers, and his "law of bounded change" isolates the essential property of the traditional mean-value theorem in an easy-to-use form. The book begins with simple concepts revolving around interval arithmetic, considers many examples, and proves elementary propositions. Chapter 1 is devoted to proving results, and the great advantage of devoting this time and space to numerous examples is that the reader gets practice producing proofs of relatively easy concepts before having to deal with complicated notions such as continuity and differentiability. The author dedicated many pages to this material knowing that it will pay dividends later. Not only does it provide a gentle introduction to reading carefully and constructing proofs, but the interval arithmetic it develops has important applications to studying error propagation in the physical sciences; there are important applications in computer science as well. As a capstone to this introductory by pedagogically important material, a real number is defined to be a fine and consistent family of rational intervals.
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