NUMBER SYSTEM
A number system is defined as a system of writing to express numbers.
✹ Types of Number
1. Natural Number: ପ୍ରକୃତ ସଂଖ୍ୟା (N)
All counting numbers are called Natural number.
Example: 1,2,3,4,5,6,7,8,910…….∞
2.Whole Number: ପୂର୍ଣ ସଂଖ୍ୟା (W)
Whole Numbers are simply the numbers
Example: 0, 1, 2, 3, 4, 5, …∞
3.Integer : ଅଖଣ୍ଡ ସଂଖ୍ୟା (Z)
Integers are like whole numbers, but they also include negative numbers.
Example:∞…-5,-4,-3,-2,-1,0,1,2,3,4,5…∞
4. Rational Number: ପରିମେୟ ସଂଖ୍ୟା (Q)
Any number that can be written as a fraction is called a Rational Number.
Rational Numbers p/q : p and q are integers, q does not = zero (0).
Example: -2/7,-8/13,0.6 etc.
5.Irrational Number: ଅପରିମେୟ ସଂଖ୍ୟା
All numbers which can’t be written as fraction.
Example: √2,√3,√7,π,0.1313313
6.Real Number :ବାସ୍ତବ ସଂଖ୍ୟା (R)
Real numbers include both Rational and Irrational Numbers.
Example: -3,-1,0,4,π,√3,1.1 etc.
7.Complex Number
Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and ‘i’ is an imaginary number called “iota”. The value of i (√-1).
Example: ..,-3+2i,1+2i
8.Perfect Number :
A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.
Example: 6,28,496,8,128
9.Twin Prime ଯୁଗ୍ମଜ ମୈଳିକ
Two prime numbers whose difference is 2 are called twin primes.
Example: (3,5),(5,7),(11,13)
10.Co-prime ଯମଜ ମୈଳିକ
Two number whose H.C.F is 1 are called co-prime numbers.
Example: (2,3),(8,9)
★ Important Notes:-
➤ All natural numbers are whole numbers.
➤ All whole numbers are not natural numbers.
➤ The smallest prime number is 2.
➤ The only even prime numbers is 2.
➤ The first odd prime number is 3.
➤ 1 is a unique number- neither prime nor composite.
➤ The least composite number is 4.
➤ The least odd composite number is 9.