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IN1004 Mathematics for Computing Lecturer: Dr. Peter W.H. Smith peters@soi.city.ac.uk 1. Set Theory 1.1 Introduction A set is one of the most fundamental cornerstones of mathematics. It is a well-defined collection of objects. These objects are called elements and are said to be members of the set. Well-defined implies that we are able to determine whether it is the set under scrutiny. Thus we avoid sets based on opinion, e.g. the set of all great football players. 1.2 Notation and Set membership Capital letters, A,B,C... are used to represent sets and lowercase letters are used to represent elements. For a set A, we write x ????if x is an element of A; y ????indicates that y is not a member of A. A set can be designated by listing its elements within set braces. For example, if A is the set consisting of the first five positive integers, then we write A = {1,2,3,4,5}. In this example, 2...

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