A set can be represented in three different methods:
1. Description Method. In this method, we describe the elements and this description of elements is enclosed in braces.
For example, the set of all the days of the week is written as {all days of a week}.
2. Roster Method or Tabular Form. In this method, we list all the members of the set and separate these by commas. The list is enclosed in braces.
For example, a set C of all counting numbers can be represented in roster form as, C = {1,2,3,4,5,6,...}
Note. The three dots, which is called as the ellipsis, are used to indicate the omission of some elements or to indicate that the established pattern continues without end.
3. Rule Method or Set-builder Form. In this method, the elements are not listed but they are represented by specifying a property or a general rule which is applicable to all the elements. That is, set-builder form always take the form {x l x has a certain property}.
For example, let X = {0,2,4,6,8,10,12,...}, in set builder form, we will write the set X as
X = {x l x is an even number}
which is read as "the set of elements x such that x is an even number."
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