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What is a Real Number?-Definition, And Symbol

August 8, 2022
written by Azhar Ejaz

Any number that can be found in the real world is a real number. We calculate the numbers everywhere around us. Rational numbers are used for denoting fractions, irrational numbers are used for finding the square root of a number, Natural numbers are used for counting things, integers for measuring temperature, and so on.

These distinct types of numbers make many examples of real numbers. In this lesson, we will learn all about real numbers and their important properties of real number.

What is the real number?

The set of real numbers is a union of the set of rational numbers (Q) and the set of irrational numbers ( Q’). Which is represented by R, is the so, we can write the set of real numbers as, R = Q ∪ Q’

 Real numbers include whole numbers, integers, irrational numbers, Rational numbers, Natural numbers

For example

7, 0, 2.3, 4/3, √and 3, are real numbers

Definition of Real number

Real numbers include rational numbers like negative integers and positive integers, fractions, and irrational numbers. The numbers that are neither irrational nor rational are non-real numbers, like, √-1, 8+ 5i, and

 -i. These numbers include a set of a complex numbers.

The subset of Real numbers

All numbers are real numbers except complex numbers.  Therefore, real numbers have the following five subsets:

  • Natural number
  • Whole number
  • Integers
  • Rational number
  • Irrational number
image showing the subset of the real number

Symbol of real numbers

Real numbers are denoted by the symbol R. Here is a list of the symbols of the subset of real numbers

  • N=natural number of set
  • W=whole number of set
  • Z=integers
  • Q=rational number
  • Q’=irrational number

Real numbers line

A number line helps us to display numbers by denoting a unique point on the line. Every point on the number line shows a unique real number. Note the following steps to denoting real numbers on a number line

  • Draw a horizontal line with arrows on both ends and mark the number zero (0) in the middle. The number zero( 0 )is called the origin.
  • Mark an equal length on both sides of the origin and label it with a definite scale.
  • It should be noted that the positive numbers lie on the right side of the origin and the negative numbers lie on the left side of the origin
image showing the real number line


  • A rational number is a subset of a real number, every rational number is a real number
  • An irrational number is a subset of a real number, every irrational number is a real number
  • All numbers are real numbers except complex numbers
  • The set of integers and natural numbers and the set of real numbers also satisfies the closure property, the commutative property, the associative property, and the distributive property. The properties of real numbers.
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