Check sibling questions

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)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.