The Weierstrass Function
converges uniformly on R and de nes a continuous but nowhere di erentiable function. The function appearing in the above theorem is called theWeierstrass function. Before we prove the theorem, we require the following lemma: Lemma (The Weierstrass M-test). Let (E;d) be a metric space, and for each n2N let f n: E !R be a function.
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