Properties of supremum and infimum

 1) Uniqueness property
  The suprumum and infimum of a bounded subset S of Ɍ, if exist is unique.

2) Approximation Property
 Let A be a non- empty set  in Ɍ which is bounded abouve and b = sup A. Then for any c ˂ b there exist x in A such that c ˂x≤ b.

3) Additive property
Let two non - empty sets  A  & B are given. Let C = { x+ y: x ɛ A and y ɛ B} . If each of A & B has supremum  then  C has also supremum  and SupA + supB = supC.

4) Comparison  property
Let  A & B be two sets in Ɍ such that x ≤ y for all x belongs to A and for all y belongs to B. If  B has supremum hence SupA ≤ supB.

   

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Filed Under: Mathematics on Saturday, July 18, 2015 No Comments

Two differences between supremum and Infimum

Let A be a set in Ɍ (set of all real numbers) . 
A number b said to be supremum if 
1)  b  is upper bund for set A  but to be infimum  b is lower bound for set A.
2)Every number less than b is not an upper bound for set A.    On the other hand, every number greater than b is not lower bound for A. 
Example,
A = {1, 2, 3, 4}
Here, Supremum of set A  is 4 and infimum of set A is 1.

Note that supremum also known as least upper bound and infimum also known as gratest lower bound.

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Top Three levels of management

 1) Top Management

2)  Middle management

3)  Lower Management

       

                                                                               source:http://tse1.mm.bing.net/th?&id=JN.oXI08oAJuI3ddFCtJ/qT%2bA&w=300&h=300&c=0&pid=1.9&rs=0&p=0

 Top management of an organization consists of board of directors, chairman, managing director and general managing director .The important functions of it includes: 

* Determine the goal of an organization

* To make polices..

* To provide overall directions in the office.

* to exercise effective control of the operations etc.

   

 Middle Management consists of departmental , divisional and section heads attached to the different departments and sections. Manly they have the responsibility for implementing and controlling plans and strategies as developed by the top management.TO Interpret polices, recruit and select suitable operative, to  assign duties an responsibilities for  plans and so on are the function of middle management.

    Lower Management consists of foremen, supervisor, sales officers, account officers etc.The are responsible for the implementation and control of the operational plans developed by middle managers.

To classify and assign jobs to the workers, direct and guide the workers about work procedure, issue orders and instructions on  the operatives and to supervise and control their work,arrange the necessary tools,equipment  and to solve the problems of workers are the major functions of lower management.

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Major ten features of management

  
 source :http://www.thestaffingstream.com/wp-content/uploads/2012/12/supplier-management.jpg

1) Goal-oriented                                                  

Management is managing people and other resources in the organization for achieving the goals of the organization. All managerial activities are directed in the  accomplishment of goals. The basis goal of management is to maximize efficiency and economic oh human efforts.

2) Group activity
Management can not be done in isolation. It always refers to group efforts.Whenever there is an organized group of people working towards a common goal.

3) Distinct process
Management is required in all types of  organization. The basic principles of management are applicable business as well as in other organizations.

4) Universal activity
It is required all types of organization. Principles are flexible and are modified according to the needs and environment of the organization.

5) An integrating process
The essence of management is integration of human and other resources for effective performance.It integrates men, machines and materials for carrying out the operations for achieving the  goals.

6) Management is a social process
It is a social process because it consists of getting things done through others. This involves dealing with people. Management has a social obligation to make optimum use of scarce rescources for the benefit of the community as a whole.

7) It is both science &art
Management is science because it ha developed certain principles that are of universal application.It is also an art because the result of management depend upon the personal skill of managers.

8) Management is a profession
It has a systematic and specialized body of knowledge ,principles and techniques which can be taught as well as applied in practice.

9) it IS Dynamic
Obviously it is a dynamic function, has to be performed continuously.It operates even in an ever - changing environment.

10) Management is intangible
It is an unseen forces but its result are apparent. It is judge on the basis of the end result althogh operations can not be  observed.

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Five tips of learning

Learning about any subject or matter is not easy ,but we try to make it easy. In the world the term 'impossible ' is disappearing day by day due to modern technology, inventions, like computer,email, internet and so on.
To now about any topics first of all we have to be hungry,not to eat but to know about the subject.If you heard something about your topic ,you can encountered with them in your own way. A desire to learn is another important things. Many research, inventions, have been success because of an interest. There are few steps of learning, let's discuss !

1) Interest
Learning is main part of our life. when you are going to learn about any topic or subject, you can create suitable  routine , think some motivational quotes to be interested in the topic. Your interest can create various ways, formula to reach the conclusion.

2)  See from the different angles
You can collect the information by using various tools and techniques but to be analysis them from the different ways. Remember that both part of the coin are true.for example, an old woman always reads newspaper more than on hour.can you guess what she reads in newspaper ? you say news but i say 'no' . you give other answers like read advertisements, important phone numbers, articles, opinions, watch cartoon,........,............, ...  But my answer is no,no,...........no.. But the true answer is she reads sympathy in the newspaper.

 3)  Goal setting
What is your goal  ?  For what purpose you are going to learn ? And you know that without any goal you are just like monkey. Goal setting force you to create many ideas.

4) Motivation
Read books about famous people. Write motivational quotes in chart-paper ,put it infront of you when you feel boar, you can see it. It makes you fresh. Motivating yourself and others everyday.

5) Join learning group
There are many group pages in social side such like facebook, tweeter, and so on.you can ask many question for your answer. In such side you can share many kind of ideas.opinion, views etc.
In sum up, these are some tips to make your future bright. Apply from today till you are in this world.

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on Monday, July 13, 2015 No Comments

How can i involve in an online college degree?

As we know that An online degree is an academic degree which can be gained through internet connected computer.  Most of the testimonials, materials found in internet. There is no need to go college and take the class. 

But the main point is that  "any person can involve on it?" No, first of all we have computer knowledge and skill to search many course related references. we shall do our homework and give our exam through online. So our typing skill should be fast. There are many colleges, people can apply through online and fulfill their minimum requirement such as fee and other activities.

There are many people can not attain the class due to their works.such people are like army, police,housewife,physically weak people etc.So online degree and   and certificate programs are designed for individuals who are seeking an alternative to the on-campus experience and are expecting the same challenging courses and the same prestigious degree as those who attend our traditional on-campus programs.

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on Wednesday, July 8, 2015 No Comments