Open Interval and Closed Interval - Definition, Examples, Quiz, FAQ, Trivia
Let's learn about number ranges and how to write them like a math pro!
What is an Interval?
Hello there! Have you ever wanted to talk about a whole bunch of numbers all at once, without having to list every single one? That's where intervals come in! In math, an interval is a range of numbers between two given numbers. Think of it like a piece of a number line.
For example, instead of saying "4, 5, 6, and 7", we can use an interval to talk about all the numbers between 3 and 8. But here's an important question: do we include the 3 and the 8? Let's find out!
Closed Intervals
A closed interval is a range of numbers that includes its endpoints. The "closed" part means the doors are closed and the endpoints can't get out—they are part of the group!
We use square brackets [ ] to show a closed interval. On a number line, we use filled-in circles (●) to show that the numbers are included.
![A number line showing the interval [2, 7]. There are solid, filled-in circles at the numbers 2 and 7, and the line between them is shaded blue. The text '[2, 7]' is written below the number line.](https://assets.workybooks.com/INTERACTIVE/media/1758607126846-72383376-interval-2.webp)
The interval [2, 7] means all the numbers between 2 and 7, including 2 and 7. So, numbers like 2, 3.5, 5, 6.1, and 7 are all in this interval.
Open Intervals
An open interval is a range of numbers that does NOT include its endpoints. Think of it like a path with open gates at the ends—you can get really, really close to the endpoints, but you never actually stand on them.
We use parentheses ( ) to show an open interval. On a number line, we use empty circles (○) to show that the endpoint numbers are not included.
The interval (1, 6) means all the numbers between 1 and 6, but NOT including 1 and 6. So, numbers like 1.01, 2, 4.5, and 5.99 are in this interval, but 1 and 6 are not.
Intervals Quiz
Ready to test what you've learned? Choose the best answer for each question.
Frequently Asked Questions
Math Trivia
Ancient Symbols
The parenthesis symbols ( ) were first used to group numbers way back in the 1500s. The square brackets [ ] came along a little later. They have been helping mathematicians keep their work tidy for centuries!
Who Invented Infinity?
The infinity symbol (∞) was first used in the 1650s by an English mathematician named John Wallis. He also helped develop the idea of the number line, which is so helpful for understanding intervals!
Not Just For Numbers
The idea of intervals is used in other areas too! In music, an interval is the distance between two notes. In language, it can be a pause or a space. It's all about what's in between!
