Real Numbers

Real numbers can be defined as the union of both the rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.


The table shows the sets of numbers that come under real numbers.

Number setIs it a part of the set of real numbers?
Natural Numbers
Whole Numbers
Rational Numbers
Irrational Numbers
Complex Numbers

Symbol of Real Numbers

Real numbers are represented by the symbol R. The list of the rest of the numbers are as follows:

  • N – Natural numbers
  • W – Whole numbers
  • Z – Integers
  • Q – Rational numbers
  •  – Irrational numbers


Are there Real Numbers that are not Rational or Irrational?

No, there are no real numbers that are neither rational nor irrational. The definition of real numbers itself states that it is a combination of both rational and irrational numbers.

Is Zero a Real or an Imaginary Number?

Zero is considered as both a real and an imaginary number. As we know, imaginary numbers are the square root of non-positive real numbers. And since 0 is also a non-positive number, therefore it fulfils the criteria of the imaginary number. Whereas 0 is also a rational number, which is defined in a number line and hence a real number.

Is the real number a subset of a complex number?

Yes, because a complex number is the combination of a real and imaginary number. So, if the complex number is a set then the real and imaginary number are the subsets of it.

Demonstrated below is a simplified way to classify numbers. It can be used as a basic template for the steps to be followed in order to aid the learners.


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