High Quality Content by WIKIPEDIA articles! In mathematics, Volterra's function, named for Vito Volterra, is a real-valued function V(x) defined on the real line R with the following curious combination of properties:The function is defined by making use of the Smith Volterra Cantor set and "copies" of the function defined by f(x) = x2sin(1/x) for x 0 and f(x) = 0 for x = 0. The construction of V(x) begins by determining the largest value of x in the interval [0, 1/8] for which f (x) = 0. Once this value (say x0) is determined, extend the function to the right with a constant value of f(x0) up to and including the point 1/8. Once this is done, a mirror image of the function can be created starting at the point 1/4 and extending downward towards 0.