devotion & mathematics

                                                  AREA OFSUBSETS OF R 2 Area of a Rectangle in R 2   :                             In R 2 , the rectangle is defined as the set {(x, y)/a≤ x ≤ b, c≤ y≤ d}.                                                    The area is (b-a)(d-c). Area of a bounded subset in  R 2   which is not a rectangle :                                               ...

contents : 1. Extended real number system 2. The symbol infinity 3. Properties of infinity THE EXTENDED REAL NUMBER SYSTEM :                                    Basically the real number system not contain + or -  ∞, it  contains all the real numbers lies between for - ∞ and + ∞ i.e.  the real number system R=(- ∞. ∞).                                     The extended real number system is a union of the real number set R and the symbols - ∞ and + ∞ i.e. Extended real system = R ⋃ {- ∞, ∞} = [- ∞, ∞]    In extended real number system,  ∞ is an upper bound   and - ∞ is a lower bound of every subset. Here we see an example to tell the main difference between real and extended real number systems.     Consider an open interval (2, ∞).  The interval (2, ∞) i...

  BASIC DEFINITIONS :                                      In this session , I am going to give definitions and few examples of   * set  * upper bound of a set  * lower bound of a set  * greatest lower bound or infimum of a set  * least upper bound or supremum of a set  * bounded above, bounded below and  bounded sets.  * Diameter of a set.  * Distance between a point and a set   SET :         A set is a collection of numbers or elements or objects etc.       For example :               * the collection of numbers which contain 1,2,3,... is called the set of natural numbers.              * The  collection of all people aged between 25-30 is called a set.              * The colle...