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 :
Which of the following collection are sets ? Justify your answer.
Question 1 :
A collection of all natural numbers less than 50.
Answer :
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
Answer :
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.
Answer :
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
Answer :
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.
Answer :
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
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