Definition Of Set And Elements Of A Set

A Set:
A set is a collection of well-defined and well-distinguished objects. From a set it is possible to tell whether a given object belongs to a set or not. The following are some illustrations of a set:

• The possible outcomes in the toss of die
• The Integers from 1 to 100
• The vowels in English alphabets

The basic characteristics of a set are that it should be well-defined; its objects or elements should be well- distinguished for easy recognition by description.

Elements Of A Set:
The object that makes up a set are called the members or elements of the set. It is almost a convention to indicate sets by capital letter, like A, B, C or X, Y, Z while the elements in the set by smaller or lower case letters, viz.., a, b, c or x, y, z. Now, to indicate that a particular element or object “ belongs to a set “ or “ a member of the set ” we use the Greek symbol capital epsilon ∈.
For example if x is the member of a set A, We shall indicate it symbolically as:
x∈A,i.e.,x is a member Or an elements of the set A