## INTRODUCTION TO SET

We often deal with a group or a collection of objects,  such as a collection of books, a collection of English alphabets, a group of students, a list of states in a country, a collection of coins, etc. Set may be considered as a mathematical way of representing a collection or a group of objects.

Definition of Set :

A set is a collection of well defined objects. The objects of a set are called elements or members of the set.

The main property of a set is that it is well defined. This means that given any object, it must be clear whether that object is a member (element) of the set or not.

Generally, sets are named with the capital letters A, B, C, etc. The elements of a set are denoted by the small letters a, b, c, etc.

Examples of Sets in Daily Life :

• Students in our class room
• Collection of animals in the world
• Collection of fruits
• Collection of vegetables

Question 1 :

A collection of all natural numbers less than 50.

If forms a set. The set will have the following elements.

A = {1, 2, 3, 4, 5, ...................50}

Question 2 :

A collection of good hockey players in America

If doesn't form a set. Because the term "Good player" is vague and it is not well defined.

However a collection of players of hockey is a set.

Question 3 :

A collection of all girls in our class.

If forms a set. The elements of the above set is the names of those girls in the class.

Question 4 :

A collection of prime numbers less than 30

If forms a set.  The set will have the following elements.

A = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }

Question 5 :

A collection of ten most talented mathematics teachers.

If doesn't form a set. Because the term "Most talented" is vague and it is not well defined.

However a collection of players of hockey is a set.

In this chapter we will have frequent interaction with some sets, so we reserve some letters for these sets as listed below. :

N  :  The set of natural numbers

Z  :  The set of integers

Z+  :  The set of all positive integers

Q  :  The set of all rational numbers

Q+  :  The set of all positive rational numbers

R+  :  The set of all real numbers

R+  :  The set of all positive real numbers

C  :  The set of all complex numbers Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. Kindly mail your feedback to v4formath@gmail.com

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