Real Numbers Definition

Such values that are not complex or imaginary and can be represented as terminating or non-terminating decimal expansions are real numbers.
Why real numbers are called "Real Numbers"?
Real numbers are called so because they are important part of our real life and are used for making measurements such as calculating attributes of anything like distance, cost, temperature, weight , length , width etc.

 Let's check for all real numbers symbol

The symbol ℝ is used as all real numbers symbol.

Difference between real and complex numbers:

The word ‘real’ distinguishes the real numbers from complex or imaginary numbers ( as discussed in real numbers definition )which are used to define the mathematical interpretations of certain effects such as those in electric phenomena. The complex numbers are represented by ‘i’ which is called iota where

iota formula

Real numbers can be ordered (true for both rational and irrational numbers) which is not valid in case of imaginary numbers. For Example : The numbers 1,7,3 can be ordered as 1,3,7.


Now , let’s discuss what is a real number or what numbers are included in real numbers.

Real numbers include rational and irrational numbers where rational numbers include positive and negative integers , whole numbers , natural numbers ,fractions and decimals [terminates or have repeats]. Irrational numbers include decimals expansions that never terminate and never have repetition of digits. The infinity of irrational numbers is greater than rational numbers.

Examples of real numbers

1. 22 or 4 ( rational and natural)

2. 1 /2 or 0.5 (rational )

3. root of twoor 1.414…. (irrational)

4. -1/10 or -0.1 (rational , negative integer)

5.Pi number (irrational )

6. 0/2 (rational ,whole number , integer )


More topics in Real Numbers
Properties of Real Numbers Real Numbers Examples
Subsets of Real Numbers
Ian Roberts
San Francisco, USA

"If you're at school or you just deal with mathematics, you need to use This thing is really helpful."
Lisa Jordan
Math Teacher
New-York, USA

"I will recommend Studygeek to students, who have some chalenges in mathematics. This Site has bunch of great lessons and examples. "
John Maloney
Student, Designer
Philadelphia, USA

" I'm a geek, and I love this website. It really helped me during my math classes. Check it out) "
Steve Karpesky
Vancuver, Canada

"I use a lot on a daily basis, helping my son with his geometry classes. Also, it has very cool math solver, which makes study process pretty fun"