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
Video Examples: Open and closed intervals
Solved Example on Open Interval
Ques: Identify the interval that represents the shaded part of the number line shown.
A. (- 3, 2)
B. [2, - 3]
C. [- 3, 2]
D. (2, - 3)
Correct Answer: A
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.