Main Page | See live article | Alphabetical index A devil's staircase is a function f(x) defined on the interval [a,b] with the following properties: f(x) is continuous on [a,b]. there exists a set N of measure 0 such that for all x outside of N the derivative f ′(x) exists and is zero. f(x) is nondecreasing on [a,b]. f(a) < f(b). A standard example of a devil's staircase is the Cantor function, which is sometimes called "the" devil's staircase. There are, however, other functions that have been given that name. One is defined in terms of the circle map. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.