OPEN INTERVAL
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.
Quick Summary
- Open intervals exclude their endpoints.
- They are denoted using parentheses ( ).
- An open interval (a, b) represents all real numbers strictly between a and b.
🍎 Teacher Insights
Emphasize the visual representation on a number line to help students understand the exclusion of endpoints. Use various examples with different number sets (integers, rationals) to solidify the concept.🎓 Prerequisites
- Real Numbers
- Inequalities
- Number Line
Check Your Knowledge
Q1: Which of the following represents the open interval containing all numbers between -1 and 3, excluding -1 and 3?
Q2: Which of the following numbers is NOT included in the open interval (0, 5)?
Frequently Asked Questions
Q: How do I represent all numbers greater than 5 on a number line?
A: If 5 is excluded, use an open interval (5, ∞). On a number line, use an open circle at 5 and shade to the right.
Q: Is (2, 2) a valid open interval?
A: No, an open interval (a, b) requires a < b. Also, (2,2) would be empty.