Interval notation

Use the table below in order to understand interval notation in math. An interval is a set containing all numbers between two given numbers.

The set may have one, both, or neither of the two given numbers.

Interval notation


An interval is open if the interval does not contain its endpoints. An interval is closed if the interval contains its endpoints. 

Sometimes, the interval may contain only one of its endpoints. In this case, the interval is half-open.

Notice the symbol ∞ which mean infinity.

-∞ means minus infinity and +∞ means positive iinfinity.

Why do we need intervals? They can be used to describe the domains of functions, bounds for estimates, and the solution sets of equations and inequalities. 

The length of an interval with endpoints a and b with a < b is b - a.

The interval [2, 8) contains 2 and all numbers between 2 and 8. Notice that 8 is not included since the interval is open at 8.

Recent Articles

  1. How to Write an Inequality

    Dec 12, 19 07:51 AM

    Learn how to write an inequality quickly with this easy to follow math lesson.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.