Abstract
The examples of continuous nowhere differentiable functions given in most analysis texts involve the uniform convergence of a series of functions (see Hobson [1, pp. 401412]). In the last twenty years interest in this subject has been renewed ([2]-[7]). In this note we constlruct a new elementary example by using the Cantor series, which is very accessible and needs only the basic notion of limit. Let qn > 2 be a sequence of positive integers. A Cantor series, or Cantor expansion, for a real number x E [0, 1] is analogous to a decimal expansion, where numbers other than powers of ten can serve as denominators:
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