Real Numbers

Real numbers? Sounds strange? How can numbers be real or not real? Let us understand the magic of numbers:

Real number (R) is a big bucket in which you pour in:

  1. Natural Numbers (N)

  2. Whole Numbers (W)

  3. Integers (Z)

  4. Rational Numbers (Q)

  5. Irrational Number



I am sure, many more questions must be bothering you, like what are these  different numbers?

  •  We know, Natural Numbers are the positive numbers starting from 1, i.e. 1,2,3…..

  • 0 plus all the natural numbers makes the set of Whole Numbers, i.e. 0, 1,2,3…..

  • All the negatives of the natural numbers and the whole numbers make up the Integers, i.e. ….-3, -2, -1, 0, 1,2,3…..

All these numbers can be represented on the Number Line. But does it complete the number line?

Every point on the number line represents a Real Number

What are these fractional numbers? What is  ๐…?

Any number which can be represented in the form of p/q , where q ≠ 0, is known as rational numbers.

            Like 3/4 , 25 = 25/1

So we can say, every integer is a Rational Number.

๐… = 3.1459……. 

So we can understand, ๐… is a number, which cannot be expressed in simple fractions.


What about the numbers which cannot be expressed in the form of p/q?

These numbers are known as irrational numbers, like, ๐… , square root of a non – perfect  square (√3)

Does this mean, every number is a Real Number?


No, there are numbers, which are not real.

The non - real numbers are;

  • Imaginary numbers, like the square root of -1 (√-1)

  • Infinity 


Learn more about real numbers from



Himanshu Agrawal
B. Tech, IIT Kanpur (2000)


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