Reviews for Number systems and the foundations of analysis

The average rating for Number systems and the foundations of analysis based on 2 reviews is 5 stars.

Review # 1 was written on 2020-08-15 00:00:00 Robert Burchill It’s a college textbook, but a very readable one. If you ever wanted a know how to rigorously derive real number arithmetic from first principles, boy is this ever the book for you! Starting with the Peano axioms (roughly speaking, they provide characterizations of “first”, “next”, and “all”) plus some basic set theory and logic, the book defines whole number addition and multiplication, and then negative numbers/subtraction, rational numbers/division, and finally real number arithmetic. If this sort of thing sounds at all appealing, I highly recommend it. The strictly mathematical prerequisites are low: advanced techniques are developed as needed. In principle, there’s nothing here that a sufficiently motivated high school student couldn’t follow, although some familiarity with mathematical proofs would be very helpful.

Review # 2 was written on 2018-05-08 00:00:00 Tim Gardner I read the 1973 Academic Press edition (not the Dover edition). This book should be a model for how a math textbook is written. It is extremely clear and complete. The typesetting is immaculate. The book contains fewer errors and typos than any other textbook I've read. Everything is proven with the utmost rigor. University math departments usually have a course that serves as a bridge between the lower-level courses and upper-level courses like real analysis and abstract algebra. This book deserves to be assigned reading in all such courses. Every aspiring mathematician needs to know that a complete ordered field exists and that the theory of complete ordered fields is categorical. If you are a mathematics major, stop taking the real number system for granted and read this book.