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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

KEY TERMS

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Continuous

—The property of a function that expresses the notion that it is unbroken in the sense that no points are missing from its graph and no sudden jumps occur in its graph.

Additional topics

Science EncyclopediaScience & Philosophy: Incomplete dominance to IntuitionismInterval - Notation, Applications