Open Interval
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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.
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.
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