number system

                               Number System

Generally number system is divided into tow parts.       
A) Real number    B) Imaginary number

Again Real number is divided into tow parts.

a) Rational   b) Irrational

 

a) Rational-     Rational number are those that are in the form of p/q i.e. 1/2,  3/5,  0.2, 1, 3, 4

Again we can divide rational number into two broad category.

1) Integers    2) Fraction or decimals (including only terminating decimal and non-terminating repeating decimal)

1)Integers

 

Integers are divided into three broad category.

a) positive integers  { 1,2,3,4,5...............}
b)  zero integer  {0}
c) Negative integers {-1,-2,-3,-4..............}

These are some specific set of integers.
Whole number -  {0,1,2,3,4,5..................}
Natural number   {1,2,3,4,5,6...................}
Even number -Which are divisible by 2.              {2,4,6,8..........................}

Odd number - Which are not divisible by 2         {1,3,5,7,9.................}
prime number - which are divisible by 1 or itself   {2,3,5,7,11,13,................}

2 ) fraction or decimals (including only terminating decimal and non-terminating repeating decimals )

we can understand this concept with these simple examples
1/2 = 0.5  fraction and terminating decimal
1/3 = 0.33333333333............ fraction and  non-terminating repeating decimal

b) Irrational number  (including non-terminating and non-repeating decimals)

 That cannot be in the form of p/q

For example we can't write root 2 into p/q form because value of root 2 {root 2 = 1.414...........} is non-terminating and non-repeating. similarly root 3, root 5, are also non-terminating and non-repeating so they are also irrational

value of π  is 22/7 approx., . π is an irrational number since π is ratio of two irrational numbers.

 

B) Imaginary numbers

we can only imagine those numbers, for example all roots of negative numbers are imaginary numbers.