OPEN SENTENCE

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.