Introduction to Set Theory

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Today's topic is :

Introduction to Set Theory!

• This theory was developed by German mathematician George Cantor.

• Fundamental part of present day mathematics.

• Used in almost every branch of mathematics.

• Used to define concepts of relation and functions

Definition:

A set is a collection of objects of similar kind.

OR

A set is well-defined collection of objects.

Example: A pack of cards, a crowd of people and a cricket team, etc.

Some Important Sets...

1. N : The set of all natural numbers.
2. Z : The set of all integers.
3. Q : The set of all rational numbers.
4. R : The set of real numbers.
5. Z+ : The set of positive integers.
6. Q+ : The set of positive rational numbers.
7. R+ : The set of positive real numbers.

Points to Remember:

• Elements , Objects and Members of sets are synonymous.
• Sets are denoted by capital letters A, C, X, Y, etc.
• Elements of sets are denoted by small letters a, b, c, x, z, etc.
• Each element can only be used one time.
• If there is a set A with elements a,b,c then:

We can say that ‘a ∈ A’ i.e. ‘a belongs to A’

And

     ‘d ∉ A’ i.e. ‘d doesn’t belongs to A’

Practice:

Q. Which of the following is not a set?

1) The collection  of all boys in your class.

2) The collection of all integers.

3) The collection of all natural no. less than 100.

4) The collection of best batsman in the world.

Ans. 4 because it is not particular answer. Different people may have different favourite or best batsman.

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