A Nowhere Differentiable Continuous Function

Abstract

The examples of continuous nowhere differentiable functions given in most analysis texts involve the uniform convergence of a series of functions [1, pp. 401-412]. In the last twenty years this subject has again received a good deal of attention; see [2]-[6]. The purpose of this note is to give a new elementary example that needs only the basic notion of limit and is very accessible and appropriate for a first calculus course. For each real number x E [0, 1], let its base-b expansion be