Set - An introduction

In our mathematical language, everything in the universe(living or non-living) is called as an object.

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

By well defined, we mean that it must be possible for one to decide that an object belongs to that collection or not.

The objects in a set are called its members or elements.

Sets are denoted by capital letters as A, B, C etc. and their elements are denoted by small letters a, b, c etc.

Consider a set A and let ‘a’ is a member of it, then we write it as a ϵ A.

The symbol ϵ stands for belongs to or is a member of or is an element of.

a ϵ A is read as a belongs to A or a is a member of A or a is an element of A.

As b is not a member of A. so we write as b ɇ A.

b ɇ A is read as b  does not belongs to A or b Is not a member of A or b is not an element of A.

Examples :

The collections which are sets are:

Ø  Collection of the rivers in India.

Ø  Collection of vowels in English alphabets.

Ø  Collection of numericals in your mathematics book.

Ø  Collection of students in your school.

Ø  Collection of notebooks in your bag.

Ø  Collection of all states of India.

Ø  Collection of natural numbers.

Ø  Collection of factors of 214.

The collections which are not set are :

Ø  Collection of intelligent students of your class.

Ø  Collection of best cricket batsman in Indian cricket team.

Ø  Collection of beautiful girls in the world.

Ø  Collection of dangerous animals in the world.

Ø  Collection of rich persons in India.

Ø  Collection of famous writers in the world.

The above collections are not sets as the words intelligent, best, beautiful, dangerous, rich and famous are not well defined.