devotion & mathematics

  Some important subsets of R . We define some important subsets of R the set of real numbers , namely 1. Inductive Set 2. The set of natural numbers 3. The set of Whole numbers             4.The set of integers                                                 5.The set of rational numbers 6.The set of irrational numbers   in different manner. Inductive set :    If A is a subset of R is  such that      i) 1  Ꜫ A    ii) p  Ꜫ A implies p+1  Ꜫ A , then A is called an Inductive set. Examples and counter examples :  1.  The set R, of real numbers is an inductive set.  2. the set  Z +  of all + ve integers is an inductive set. 3. the set  Z -   of all -ve integers is not inductive since 1  ∉  Z - Natural numbers : ...

Real  Number System :                              In mathematics mainly there are two kinds of number systems. They are  1. Real Number System. 2. Complex Number System.    About complex number system we discuss later.  Here I introduce about what is a Real number system i.e. what are called the real numbers. The real number system includes basically  the set of all rational and irrational numbers i.e the set of real numbers is an union of set of rational numbers and the set of irrational numbers. But there are some subsets are there for the set of all rational numbers. They are set of natural numbers, set of whole numbers, set of integers.  Therefore the set of Real Numbers is a combination of  1. set of natural numbers 2. set of whole numbers                                    ...