Fundamentals

This chapter introduces some elementary facts from set theory, topology of the real numbers, and the theory of real functions. The concepts of real analysis rest on the system of real numbers and on notions such as sets, relations, and functions. A set is a well-defined collection of objects. The objects in the collection are called the elements of the set. For example, A is equal to {x, y, z} is a set with three elements x, y, and z. The notation x Є A denotes that x belongs to A or, equivalently, x is in A . The set of natural numbers is denoted by N , the set of integers by Z , the set of rational numbers by Q , and the set of complex numbers by C . For two sets A and B , A is called a subset of B , denoted by A I B , if every element of A is also an element of B . The intersection of two sets A and B is the set of all elements that are in both A and B , denoted by ACB .