2.1 Set Concepts 43 Listing the elements of a set inside a pair of braces, { }, is called roster form. The braces are an essential part of the notation because they identify the contents as a set. For example, { } 1, 2, 3 is notation for the set whose elements are 1, 2, and 3, but (1, 2, 3) and [ ] 1, 2, 3 are not sets because parentheses and brackets do not indicate a set. For a set written in roster form, commas separate the elements of the set. The order in which the elements are listed is not important. Additionally, we do not list an element more than once. For example, the set { } 1, 1, 2 would be written as set { } 1, 2 . Sets are generally named with capital letters. For example, the name commonly selected for the set of natural numbers or counting numbers is N. Example 2 Description of Sets Write a description of the set containing the elements Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday. Solution The set is the days of the week. ■ Now try Exercise 55 Definition: Natural Numbers { } = … N 1, 2, 3, 4, 5, The three dots after the 5, called an ellipsis, indicate that the elements in the set continue in the same manner. An ellipsis followed by a last element indicates that the elements continue in the same manner up to and including the last element. This notation is illustrated in Example 3(b). m Lake Michigan and Chicago Example 3 Roster Form of Sets Express the following sets in roster form. a) Set A is the set of natural numbers less than 5. b) Set B is the set of natural numbers greater than 10 and less than or equal to 100. c) Set C is the set of the Great Lakes. Solution a) The natural numbers less than 5 are 1, 2, 3, and 4. Thus, set A in roster form is {1, 2, 3, 4}. b) B {11, 12, 13, 14, , 100}. = … The 100 after the ellipsis indicates that the elements continue in the same manner up to and including the number 100. c) = C {Erie, Huron, Michigan, Ontario, Superior} ■ Now try Exercise 25 Example 4 The Word Inclusive Express the following sets in roster form. a) Set A is the set of natural numbers between 5 and 9. b) Set B is the set of natural numbers between 5 and 9, inclusive. Solution a) { } = A 6, 7, 8 b) { } = B 5, 6, 7, 8, 9 . Note that the word inclusive indicates that the values of 5 and 9 are included in the set. ■ Now try Exercise 29 Tetra Images/Alamy Stock Photo
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