Set Theory: The Structure of Arithmetic

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. <br>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.