The Set of Real Numbers

Abstract

This text consists of many assertions, some big, some small, some almost insignificant. These assertions are obtained from the properties of the real numbers by logical reasoning. Assertions that are especially important are called theorems. An assertion’s importance is gauged by many factors, including its depth, how many other assertions it depends on, its breadth, how many other assertions are explained by it, and its level of symmetry. The later portions of the text depend on every single assertion, no matter how small, made in Chapter 1.