Classifying sets
- 2. A set is well-defined it its elements can be specifically identified. An empty set is a set with no elements. The cardinality of a set is the number of elements in the set. Sets can be classified as finite or infinite. finite sets – elements are countable infinite sets – cannot be counted since it extends infinitely
- 3. Identifying A Well-defined And Not Well-defined Sets
- 4. Example 1. The set of counting numbers between 10 and 20. A = {11, 12, 13, 14, 15, 16, 17, 18, 19} It is a well-defined set because we can specifically list the elements of this set. Example 2. The set of nice animals. This is not a well-defined set because we cannot specifically identify the nice animals. What is nice animal to one person may not be nice to another person.
- 5. Cardinality The cardinality of a set is the number of elements in the set. If A is a set, the cardinality of set A is denoted by n(A). Set Cardinality 1. A = {11, 12, 13, …20} n(A) = 10 2. B = {x / x is a day in a week } n(B) = 7 3. C = {x / x is a vowel in the English alphabet} n(C) = 5 4. D = {5, 10, 15, 20, 25, 30} n(D) = 6 If the cardinality of a set is zero, then the set is empty.
- 6. Empty Set An empty set is a set with no elements . It is denoted by the symbol { } or ø . The cardinality of an empty set is 0. Study these examples. 1. A = { x / x is an odd number divisible by 2} A = {} or ø 2. B = { x / x is a month of a year beginning with R } B = ø
- 7. A set can be classified as finite or infinite. Study these examples: 1. A = {1, 2, 3, 4, 5, } is a finite set. 2. B = {2, 6, 6, 8, … 30} is a finite set. 3. C = {1, 3, 5, 7, …} is an infinite set. 4. D = {x / x is a counting number greater than 10} is an infinite set.
- 8. THANK YOU