Open Interval And Closed Interval
Open interval and closed interval are used to represent a range of numeric values. The open interval includes only the values between the endpoints and is represented as ( ). The closed interval includes even the endpoints of the range of values and is represented as [ ].
The open interval can be presented as an expression a < x < b, and the closed interval is represented as an expression a < x < b. Let us learn more about open interval and closed interval, their difference, real-life examples, with the help of solved examples, and FAQs.
What Is Open Interval And Closed Interval?
Open interval and closed interval represent a set of numbers. These intervals define if the end numbers of the set of numbers are included or not. In the open intervals, the set of numbers which represent the endpoints are not included, and in closed intervals, the set of numbers which represent the endpoints are included.
The open interval is represented using parenthesis - ( ), and the closed interval is represented using box brackets - [ ]. The open interval and closed interval are represented in the form of an expression. The open interval is represented as x ∈ (a, b) or a < x < b, and the closed interval is represented as x ∈ [a, b] or a < x < b.
Difference Between Open Interval And Closed Interval
The difference between open interval and closed interval can be understood based on the endpoint of the interval. A few of the difference between the open interval and the closed interval is as follows.
- The open interval does not include the endpoints, and the closed interval includes the endpoints.
- The open interval is represented using (), and the closed interval is represented using [ ].
- The expression a < x < b , represents an open interval, and the expression a < x < b represents a closed interval.
- The open interval represented on the number line has two circles at the ends, and the closed interval has a darkened dot at the end.
Examples Of Open Interval And Closed Interval
The following quick examples of open intervals and closed intervals help in a better understanding of these intervals.
- The cost of a pencil is between $2, and $4. This is an example of an open interval since it does not include the end values of $2, and $4 as the cost of the pencil.
- The admission is allowed for students between the ages of 4 years and 7 years, and it also includes students who are 4 years and 7 years old. This is an example of a closed interval, as it includes the students who are 4 years and 7 years old.
- In an examination, the students gaining more than 75% have been declared as having passed in distinction. This is an example of an open interval.
- The teacher has ordered t-shirts of sizes from 38 to 46. This is an example of the closed interval as it includes the t-shirts of sizes 38 and 46 also.
- The doctor informed the patient that he would be available for treating the patients from Monday to Friday. This is an example of the closed interval, as it includes the days Monday and Friday.
- The expression 4 < x < 9 is an example of open interval as x does not take the values of 4 and 9, but only takes the values between 4 and 9.
Related Topics
FAQs on Open Interval And Closed Interval
What Is Open Interval And Closed Interval In Algebra?
The open interval and closed interval are used in algebra to represent a range of numeric values. The open interval is represented as an algebraic expression a < x < b, and the closed interval is represented as an algebraic expression a < x < b. The open interval does not include the bounding points, and the closed interval includes the boundary points. Further the open interval is represented as ( ), and the closed interval is represented as [ ].
How Do You Represent Open Interval And Closed Interval?
The open interval is represented as parenthesis, which is ( ). And the closed intervals are represented as box brackets, which are [ ]. The open and closed intervals can also be represented as algebraic expressions. The open interval is represented as a < x < b, and the closed interval is represented as a < x < b.
What Are The Boundaries Of Open Interval And Closed Interval?
The boundaries of open intervals do not include the endpoints, and the boundaries of closed intervals include the endpoints. The open interval for the range of values (2, 3, 4, 5, 6) does not include the boundary points of 2 and 6. And the closed interval for the range of values [2, 3, 4, 5, 6] includes the boundary points of 2 and 6.
What Is The Difference Between Open Interval And Closed Interval?
The open interval is represented as ( ), and the closed interval is represented as [ ]. The open interval is represented across a number line with endpoints as circles, and the closed interval is represented across a number line with endpoints as darkened circles. The open interval and closed interval can also be represented as algebraic expressions. The open interval is represented as a < x < b, and the closed interval is represented as a < x < b.
Give examples of Open Interval And Closed Interval?
A few examples of open intervals are the height of the students in a class lies between 4 feet and 5 feet, the cost of a pen is between $2 to $5, or the time taken to reach the school from home is between 15 minutes to 20 minutes. Further, the example of closed intervals is the length of the cloth is from 1 meter to 1.2 meters, the number of students in the class is 30 or 31.