We can write

  2 < x < 5

as x ∈ (2, 5)

This is called interval notation

 

There are different types of intervals

  1. Open Interval (a < x < b)
  2. Closed interval (a ≤ x ≤ b )
  3. Semi Open Interval (a ≤ x < b and a < x ≤ b)

Interval Notation in Sets - Teachoo.jpg

 

Write x > 2 in interval notation

x greater than 2 number line.jpg

So, x goes 2 to infinity

x ∈ (2, ∞)

Note- ∞ and -∞ always has an open bracket

 

Write x ≥ 3 in interval notation

x greater than equal to 3 number line.jpg

So, x goes 3 to infinity

x ∈ [3, ∞)

 

Write x < 5 in interval notation

x less than 5 number line.jpg

So, x goes –infinity to 5

x ∈ (–∞, 5)

  

Note- ∞ and -∞ always has an open bracket

 

Write x ≤ –1 in interval notation

x less than equal to -1 number line.jpg

So, x goes –infinity to –1

x ∈ (–∞, –1]

 

Write x ≤ -1 & x > 2 in interval notation

In this, we have two notations

x ≤ –1

and x > 2

We merge both graphs

x less than equal to -1 and x greater 2 number line.jpg

So, x goes –infinity to –1 and from 2 to infinity

So, in interval notation, we write it as

x ∈ (–∞, –1] ∪ (2, ∞)

 

Write x < 5 & x > 2 in interval notation

In this, we have two notations

x < 5

x > 2

We merge both graphs

x less than equal to 5 and x greater 2 number line.jpg

So, x goes 2 to 5

So, in interval notation, we write it as

x ∈ (2, 5)

  1. Chapter 1 Class 11 Sets
  2. Concept wise
Ask Download

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail