In mathematics, the Weierstrass function is a pathological example of a real-valued function on the real line. The function has the property that it is continuous everywhere but differentiable nowhere. It is named after its discoverer Karl Weierstrass.
Historically, the Weierstrass function is important because it was the first published (1872) to challenge the notion that every continuous function was differentiable except on a set of isolated points.
Read more about Weierstrass Function: Construction, Hölder Continuity, Density of Nowhere-differentiable Functions
Famous quotes containing the word function:
“The uses of travel are occasional, and short; but the best fruit it finds, when it finds it, is conversation; and this is a main function of life.”
—Ralph Waldo Emerson (1803–1882)