Number System- Introduction

Number System is a system for representing, expressing or writing a certain type of numbers.

type of Numbers

     Complex numbers-

    A complex number is a number that can be expressed in the form (a + bi), where "a" and "b" are real numbers (b is not equal to 0), and i is a solution of the equation x² = −1. and i is Imaginary number.  in other words, real number +- imaginary number = Complex number
    for example- (5+3i)← Complex Number

    Natural numbers- 

    It is a set of counting numbers. Natural numbers are denoted by N. where,
    N=  (1,2,3,4,5....)
    Even Numbers- The set of all-natural numbers which can be divided by 2 are called Even numbers. Even numbers are denoted by E. where,
    E= (2, 4, 6, 8, 10, 12, 14, 16,.....)
    Odd numbers- It is a  set of natural numbers which are not divisible by 2. we can also say that the natural numbers which are not even numbers are Odd numbers. odd numbers are denoted by O. where,
    O= (1, 3, 5, 7, 9, 11, 13, 15......)

    Whole numbers

    when we include zero in Natural numbers, it will become the  Whole numbers. whole numbers are denoted by W, Where-
    W= (0, 1, 2, 3, 4, 5, 6, 7, 8, 9,.......)
    Integers- When in the set of whole numbers, we include negative numbers too, it will become Integers. Integers are denoted by I or Z. where,
    I= ( .......-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.....)
    Integer can further be classified into two types of Integers. Negative integers and Positive integers. Negative integers are denoted by Z- and Positive integers are denoted by Z+.
    Z- = (.....-5, -4, -3, -2, -1)
    Z+ = (1, 2, 3, 4, 5, 6......)
    0 is neither Positive nor negative Integer.
    Prime numbers- These are the set of natural numbers which have no factors except 1 or itself. in other words, we can say that Prime numbers can be divided by only themselves or 1. like, 2, 3, 5, 7, 11, etc.
    Please note that 1.- One is not a Prime number. 2.- 2 is the only even number which is also a Prime number. 3- All Prime numbers are Odd numbers, but all Odd numbers are not Prime numbers.
    Co-Prime numbers- Two numbers which have no common factors except 1, are called Co-prime numbers. Such as 9 & 16, 4 & 17 etc.
    Please note that it is not necessary that two Co-Prime numbers are always Prime numbers. They may or may not be Prime numbers.
    Composite number- Also known as Divisible numbers, is a set of whole numbers which are divisible by other than 1 and themselves. we can also say that the numbers which are not Prime numbers are Composite or Divisible numbers. Like, 4, 6, 8, 9, 10, etc.. 
    1 is neither Prime nor a composite number.

    Real numbers-

    Set of Rational and Irrational numbers are called Real numbers. The Square of all Real numbers is always Positive.
    Rational numbers- the number which can be written as a form of p/q, where both p and q are integers and Co-prime and, q is not equal to zero, is called Rational number. Rational numbers are Denoted by Q. Rational numbers can be positive or negative.
    e.g- 1/2, 2/3, -3/4, -8/9 etc.
    Irrational numbers- The numbers which are not Rational numbers are called Irrational numbers. Such as  √2= 1.414...
    and, √3= 1.732...
    and, π= 3.14...

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