Learn Number System with Free Lessons & Tips

Natural Numbers : Numbers 1,2,3,4,5,.....etc.,which are used for counting the objects are called natural numbers.

note(The number zero 0 is not a natural numbers)

WHOLE NUMBERS: All natural numbers together with 0(zero) are called whole numbers.thus,0,1,2,3,4,5,......,etc are whole numbers.

INTEGERS  All naturals numbers and negative of natural numbers with zero make a set of integers e.g...,-4,-3,-2,-1,0,1,2,3,4,....

PRIME NUMBERS  A number greater  than 1 which cannot be divided by  any other number execpt 1 and  itself,is called a prime number. e.g., 2,3,5,7,11,13,17 etc.

COMPOSITE NUMBERS Numbers  greater than 1 which are not prime are called  composite  numbers. e.g.,4,6,8,9 are all composite numbers.

note 1 is neither prime nor composite

EVEN NUMBERS  The numbers which are divisible by 2 are called even numbers.e.g.,2,4,6,8,10 etc.

ODD NUMBERS  The numbers which are note divisible by 2 are called odd numbers. e.g,1,3,5,7,9 etc

PERFECT SQUARE NUMBERS The numbers whose square root can be determined ,are called perfect square numbers. e.g.,4,36,225,...etc.

RATIONAL NUMBERS A rational number can always be represented by a fraction of the from p/q,where p and q are integers and q is not equal to zero (q≠ 0).All integers and fractions are rational numbers.e.g.,2(=2/1),2/3,3/5,7/13 etc.

IRRATIONAL NUMBERS An  irretional number can't be expressed in the form of p/q where q≠0.

√3,√2 which give only an approximate answer in the form of a fraction or decimal number.

Number System:

There are two majaor division in the Number System

i.e.

1. Real Number System

2. Complex Number System

Real Number System: (SYMBOL Is "R")

It is a set that contains following sets as subset

Natural Numbers: N = {1, 2, 3, ...}

Whole Numbers: W = {0, 1, 2, 3...}

Integers: Z = {..., -2, -1, 0, 1, 2,...}

Rational Numbers: Q = {p/q : p,q∈Z, q≠0}

Irrational Numbers: π (pi), e, and square root of natural numbers which are not a perfect squares

Note:

N ⊂ W ⊂ Z ⊂ Q ⊂ R