Set Theory pdf // mathematics pdf

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 . 

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