Sets in Mathematics: Definition and Examples

Introduction to Sets in Mathematics

Task (4 marks) In mathematics, a set is a collection of distinct elements and elements in a set are not in order. Here are some examples of sets: (a) A set of integers, e.g. integerSet = {3, 1, 4, 2} (b) A set of fruits, e.g. fruitSet = {apple, orange, papaya} (c) A set of characters, e.g. charSet = {‘A’, ‘m’, ‘&’} We always enclose elements of sets inside a pair of{ }. Here are some other properties on sets: (1)A set can be empty, i.e. no element. We call it empty set. In mathematics, we have a special symbol to denote empty set. Convenient to our design later, we will use { }to denote an empty set. (2)When checking an element is inside a set. We call it “belong to”.(3)If a set contains in another set, we call it subset. For example, {1, 2, 3} is a subset of {2, 3, 4, 6, 1}. Therefore empty set is a subset of every set. (4)The cardinal number of a set is the number of elements in a set.