Number System

Infate Academy

Number System

Natural Numbers (N)

Counting numbers are known as natural numbers N= {1,2,3,4,5…………………}

Whole Numbers (W)

Whole Numbers together with 0 form whole numbers W = {0,1,2,3,4,5……….}

Integers (I or Z)

All natural numbers, 0 and the negatives of natural numbers form the collection of integers

Z= {-$\infty$  ……….-5,-4,-3,-2,-1,0,1,2,3,4,5,…………….$\infty$}

Rational Numbers (Q)

The number of the form  $\frac{P}{Q}$ where P and Q are integers and Q$\ne$0   is in the lowest form i.e P and Q  have no common factor, is called a rational numbers.

All integers and fractions are a rational number. The set of rational numbers is denoted by Q. A rational numbers is said to be positive if its numerator and denominator are either both positive or both negative

Irrational Numbers

$\frac{5}{2}$ = 2.5 is rational number

π =3.14159… this number cannot be expressed in the form of ratio. So any number that cannot be represented in the form of ratio is called irrational number

Real numbers include whole numbers, rational numbers and irrational numbers. Real numbers can also be positive, negative and zero.

$\sqrt {-2}$    ie of any negative number is called imaginary numbers and such numbers are not real numbers

Also infinity is not a real number

Real Numbers

The collection of rational and irrational numbers are called real numbers and is denoted by R