Well-defined collection of objects : Sets #well #defined #set

 

                                  A well- defined collection of objects in the sense that we can definitely 

decide whether a given  particular object belongs to a given collection  or not. 

For example : 

 * The collection of numbers 2,4,6,8,... is  well-defined because these numbers are formed 

    by    multiply natural numbers with 2. 

 * The collection of five most renowed mathematicians of the world is not well-defined ,  

    because the criterion for determining a mathematician as most renowed may vary from 

    person to person. 

 If you have a question in your mind is that  " Is  "Collection"  a synonym to "Set" " then

   answer is " not " .

 Now we see the difference between a collection and a set. 

 " Collection " is  a general word for a group of objects. It doesn’t necessarily follow strict                            rules.

 " Set " is a well-defined collection of distinct objects.

 From the following example ,we can easily understand the difference between a collection 

 and a set.

  Collection : Nile is a member of collection of rivers in the world.

   Set : Nile is not a member of collection of rivers in India.  

  SETS :  

            The concept of set serves as 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.

                                       This theory of sets was developed by German mathematician 

George Cantor  ( 1845-1918 ). He first encoured sets while working on " problems on 

trigonometric series " .

                                                          

                                       In every day life, we often speak of collections of objects of a 

particular kind, such as , a pack of cards, a crowd of people, a cricket team , etc. In 

mathematics also, we come across collections, for example,of natural numbers, points, 

prime numbers, etc. More specially, We examine 

the following collections:

(i) Odd natural numbers less than 10 i.e.1,3,5,7,9

(ii) The rivers of India

(iii) The vowels in the English alphabet ,namely, a,e,i,o,u

(iv) Various kinds of triangles

(v) Prime factors of 210, namely, 2,3,5,7

(vi) The solutions of a particular equations 

       for example: the solution of the equation X²-5x+6 = 0 is x=2,3   etc.

 * Roaster Form 

 

    

#intermediate #set #mathematics #iit #jee #class #classxii #class12 #cbse