Interval Notation

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)

Write x > 2 in interval notation

So, x goes 2 to infinity

∴ x ∈ (2, ∞)

Note- ∞ and -∞ always has an open bracket

Write x ≥ 3 in interval notation

So, x goes 3 to infinity

∴ x ∈ [3, ∞)

Write x < 5 in interval notation

So, x goes –infinity to 5

∴ x ∈ (–∞, 5)

Note- ∞ and -∞ always has an open bracket

Write x ≤ –1 in interval notation

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

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

So, x goes 2 to 5

So, in interval notation, we write it as

∴ x ∈ (2, 5)