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

Interval Notation - Part 2

So, x goes 2 to infinity

x ∈ (2, ∞)

Note- ∞ and -∞ always has an open bracket

 

Write x ≥ 3 in interval notation

Interval Notation - Part 3

So, x goes 3 to infinity

x ∈ [3, ∞)

 

Write x < 5 in interval notation

Interval Notation - Part 4

So, x goes –infinity to 5

x ∈ (–∞, 5)

  

Note- ∞ and -∞ always has an open bracket

 

Write x ≤ –1 in interval notation

Interval Notation - Part 5

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

Interval Notation - Part 6

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

Interval Notation - Part 7

So, x goes 2 to 5

So, in interval notation, we write it as

x ∈ (2, 5)

  1. Chapter 1 Class 11 Sets (Term 1)
  2. Concept wise

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.