# Interval - Notation, Applications

###
real endpoints set closed

An interval is a set containing all the **real numbers** located between any two specific real numbers on the number line. It is a property of the set of real numbers that between any two real numbers, there are infinitely many more. Thus, an interval is an infinite set. An interval may contain its endpoints, in which case it is called a closed interval. If it does not contain its endpoints, it is an open interval. Intervals that include one or the other of, but not both, endpoints are referred to as half-open or half-closed.

## Additional Topics

An interval can be shown using set notation. For instance, the interval that includes all the numbers between 0 and 1, including both endpoints, is written 0 ≤ x ≤ 1, and read "the set of all x such that 0 is less than or equal to x and x is less than or equal to 1." The same interval with the endpoints excluded is written 0 < x < 1, where the less than sy…

There are a number of places where the concept of interval is useful. The solution to an inequality in one variable is usually one or more intervals. For example, the solution to 3x + 4 ≤ 10 is the interval (-∞,2]. The interval concept is also useful in calculus. For instance, when a function is said to be continuous on an interval [a,b], it means that the graph of the function is un…

## Citing this material

Please include a link to this page if you have found this material useful for research or writing a related article. Content on this website is from high-quality, licensed material originally published in print form. You can always be sure you're reading unbiased, factual, and accurate information.

Highlight the text below, right-click, and select “copy”. Paste the link into your website, email, or any other HTML document.

## User Comments