** Definition of Open Interval**

- Open Interval is a real number interval that does not include the end points.

**More about Open Interval**

- Open interval is denoted by the parentheses ().

**Example of Open Interval**

- On the line above, the shaded part represents the set of all the numbers between – 2 and 5. We write it as the open interval (- 2, 5).
- The open interval (5, 10) over R represents that it contains all the real numbers between 5 and 10 but does not include 5 and 10.

**Solved Example on Open Interval**

Identify the interval that represents the shaded part of the number line shown.

Choices:

A. (- 3, 2)

B. [2, - 3]

C. [- 3, 2]

D. (2, - 3)

Correct Answer: A

Solution:

Step 1:In the given line, the shaded part represents the set of all the numbers between – 3 and 2.

Step 2:It is clear that the numbers – 3 and 2 are excluded.

Step 3:An open interval represents a set excluding its end points.

Step 4:So, (- 3, 2) represents the given line.

**Related Terms for Open Interval**

- Closed Interval
- Interval
- Real Numbers