Set Theory pdf // mathematics pdf

by sayan on August 01, 2018 in mathematics

Set Theory

some contents of pdf file :

George cantor a great German mathematician developed the theory of set . This is one of the most fundamental concept of mathematics and is now used in almost all branches of science , technology , commerce , economics .

SET : A collection of well-defined distinct object is said to form a set of the object are independent of the order of their arrangements . thus, the set of vowels of English alphabet can be represent as ( a,e,I,o,u ) or in any other order .

Each of the following collection represent as set :

1. Collection of natural number : N= (1,2,3,4)

2. Collection of river of India .

3. All real number greater than 0 and less than 10

TYPES OF SET :

a. SINGLETON SET : A set which consists of one elements only is called a singleton set or unit set.

b. NULL SET : suppose a set is defined some rules or properties . the set is called a null set if there is no elements in the set satisfying the given rules . a null set is also known as empty set .

c. Finite and infinite set : a set is said to be finite if the number of elements contained in the set can be counted and the counting process has an end . in other words ., a set is said to be finite if its contains a specific number of elements . on the contrary . a set said to be infinite if the number of elements contained in the set cannot be determining by counting , clearly an infinite set does not contain a specific number of elements .