Foundations of Mathematical Analysis (Oxford Science Publications)
Oxford University Press (July 10, 1997)
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Foundations of Mathematical Analysis
covers a wide variety of topics that will be of great interest to students of pure mathematics or mathematics and philosophy. Aimed principally at graduate and advanced undergraduate students, its primary goal is to discuss the fundamental number systems, N
, and C
, in the context of the branches of mathematics for which they form a starting point; for example, a study of the natural numbers leads on to logic (via Gödel's theorems), and of the real numbers (as constructed by Cauchy) to metric spaces and topology. The author offers a refreshingly original and accessible approach, presenting standard material in new ways and incorporating less mainstream topics such as long real and rational lines and the p
-adic numbers. With a discussion of constructivism and independence questions, including Suslin's problem and the continuum hypothesis, the author completes a wide-ranging consideration of the development of mathematics from the very beginning, concentrating on the foundational issues particularly related to analysis.