Set Theory: The Structure of Arithmetic

by Norman T. Hamilton, Joseph Landin

This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. Beginning with a discussion of the rudiments of set theory, authors Norman T. Hamilton and Joseph Landin lead readers through a construction of the natural number system, discussing the integers and the rational numbers, and concluding with an in-depth examination of the real numbers.
Drawn from lecture notes for a course intended primarily for high school mathematics teachers, this volume was designed to answer the question, "What is a number?" and to provide a foundation for the study of abstract algebra, elementary Euclidean geometry, and analysis. Upon completion of this treatment — which is suitable for high school mathematics teachers and advanced high school students — readers should be well prepared for introductory courses in abstract algebra and real variables.

Genres: Mathematics

288 pages, Paperback

Published May 16, 2018

Reviews

[Steven Harmon · Rating 4 out of 5]

3 stars as an introduction to the ideas - could have used more examples or explanations of all of the proofs and concepts. It would also be difficult to read without knowledge of how to pronounce all of the notation. Slots pretty nicely as a primer for real analysis

As a reference for a teacher or something who already understands all the ideas it’s thorough and clear enough to deserve 4 stars.

[alsene · Rating 3 out of 5]

Discusses the elementary properties of sets and introduces key ideas such as the natural, rational, real numbers, explains their operations also known as binary operations.

This book was very uncomfortable to read after the half of it, it may be me, a more updated set theory book should help to overcome this issue.