# Review of Sets

A set is a collection of distinct and well-defined objects.

In general, capital letters like ** A, B, G, S, T,** etc., are used to denote

**sets**. The words aggregate, class or collection are also often used in place of the word

**set**. But the use of the word set is common. The concept of the word

**set**as described above is considered to be primitive in mathematics.

If denotes a set and is a member (or an element) of it, then we write this fact in notation form as . We read as is a member (or an element) of , or more precisely “ belongs to .” When a certain object does not belong to set we write . A set is determined by its members. Therefore, it can either be expressed by writing its various members or by assigning a certain property regarding its members so as all the members of the set are known.

The well defined, distinct and distinguishable objects (or members) in a set may be anything. When a set is described by listing all of its members, for example the set of numbers **1, 5, 17, 257**, we write it by enclosing these members within a pair of curly brackets such as . The members within the brackets may be written in any order. In case a set is described by assigning a certain property regarding its members , we shall write it as. For example, is a set of positive integers **1, 257, 65537, 4294967297**. These are two common ways of describing a set. When the specific reference to members of a set is implied, then a single capital letter may be used to denote the set. The distinctness of the members of a set holds in a conclusive sense. In specifying a set, either by means of listing its members or by assigning some property regarding its members, if a member repeats, then in the set only one representative of the repeated member is ultimately included. Thus, is actually.

**finite set**; otherwise it is called an

**infinite set**.