# Interval

## Applications

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 unbroken, no points are missing, and no sudden jumps occur anywhere between x = a and x = b. The concept of interval is also useful in understanding and evaluating integrals. An **integral** is the area under a **curve** or graph of a function. An area must be bounded on all sides to be finite, so the area under a curve is taken to be bounded by the function on one side, the x-axis on one side and vertical lines corresponding to the endpoints of an interval on the other two sides.

See also Domain; Set theory.

## Resources

### Books

Bittinger, Marvin L, and Davic Ellenbogen. *Intermediate Algebra: Concepts and Applications.* 6th ed. Reading, MA: Addison-Wesley Publishing, 2001.

Gowar, Norman. *An Invitation to Mathematics.* New York: Oxford University Press, 1979.

Larson, Ron. *Calculus With Analytic Geometry.* Boston: Houghton Mifflin College, 2002.

J. R. Maddocks

## Additional topics

Science EncyclopediaScience & Philosophy: *Incomplete dominance* to *Intuitionism*Interval - Notation, Applications