Set

Set is a well-defined collection of objects. Examples od sets

1. Players of a cricket team
2. Students of your School
3. Members of your family
4. Vowels in the English alphabet { a, e, i, o, u}
5. Prime factors of 10, namely {2,5}
6. Odd natural numbers less than 8, i.e., {1, 3, 5, 7}
7. Numbers in a Dice {1,2,3,4,5,6}

Sets in Mathematics

                N : the set of all natural numbers

                Z : the set of all integers

                Q : the set of all rational numbers

                R : the set of real numbers

The concept of set serves as a fundamental part of the present day mathematics. Today this concept is being used in almost every branch of mathematics. Sets are used to define the concepts of relations and functions. The study of geometry, sequences, probability, etc. requires the knowledge of sets.

The theory of sets was developed by German mathematician Georg Cantor (1845-1918). He first encountered sets while working on “problems on trigonometric series”.

Numerical: Let  A =  Set of all even number. Are 1, 7, 4, 9  member or not of this set.

Solution: Even number set will have numbers 2,4,6,8,10…

Numbers 1, 7 & 9 are not part of this set, while number 4 is part of this set.