#Maths Fundamentals for General competitions (Part 1. Numbers)- By NM Mishra on the behalf of Brilliant Academy of Learning Pvt Ltd (07/05/2020)#

            Number System 
1. Natural number/ Counting number/Cardinal number - 1,2,3,4,5,6,7 ......
2. Odd number -  The natural number which is not divisible by 2. Ex. - 1,3,5,7,9,11,13 .............
3. Even number - The natural number which is divisible by 2. Ex. -  2,4,6,8,10,12 .............
4. Whole number -  Every element of whole number except 0 is a natural number . 
Note - Zero is not a natural number . Zero is a whole number . Ex. -  0,1,2,3,4,5,6 .............
5. Integers - The family of integers consists of negative numbers , positive numbers and zero.  Ex. - 
......... -5,-4,-3,-2,-1,0,1,2,3,4...............
6. Composite number - The natural number which is divisible by atleast three numbers is called Composite number. Ex. -  4,6,8,9,10,12,14,15,16,18 .............
7. Prime number - The natural number which is divisible by only 1 and itself. Prime number should be divisible by neither less nor more than two numbers.
Ex. - 2,3,5,7,11,13,17,19,23,29,31 ...........
Note - 1 is not a prime number. 2 is the only even number which is prime.
8. Rational number - The number which can be expressed in the form of p upon q where there is no common factor between p and q , except 1 and q is not equal to zero. Any number divided by 0 is Infinite. Infinite is not a rational number. Standard form of any rational number requires that there should be no common factor except 1 in numerator and denominator. 
Rational number must follow one of the two following characteristics : 
(a) Terminating Decimal - When p is divided by q , division should terminate at some point . Ex. -  1/2,3/4,2/5 ...........
(b) Repetitive Decimal - When p is divided by q , numbers should repeat in quotient.
Ex. - 1/3,2/3,1/6 .............
Note - Every Integer is also a rational number. Examples of Rational number - 
-1,-2,-3,0,7,8, 2/5,3/7,4/9,6/11 .............
9. Irrational number  -  Numbers which are non- terminating and non - Repetitive are Irrational numbers. Ex - √ 2, √3 ,√ 5 , π etc.
Note - Numbers in the form of Perfect Square Root or Cube root are rational numbers. π is a irrational number because actual value of π cannot be derived . 22/7 or 3.14 is approximate value of π.
10. Real numbers - All numbers are real except negative numbers under surd . All Rational and Irrational numbers are Real numbers. Ex.  -1,-2,-3, 0, 1,2,3, 1/2,2/3, -3/5,√4,√5 etc.
11. Imaginary numbers - Those numbers which are under surds in negative form. Ex. √-2, √-3 etc. These numbers are represented as i where i is equal to √-1 .
12. Complex numbers -  Complex numbers are in the form of a+ ib where a and b are real numbers and i is imaginary quantity . The value of i is √ -1. Ex. 5+ √-2, 
4+√-3, 5+ √-7 etc.




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