Consider the set of continuous functions $\mathbb{R} \to \mathbb{R}$. I assume that the subset that are not everywhere differentiable accounts for almost all of them. Is this true? What is the precise formulation of this idea, and how do you prove it?
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2In a sense, "most" are nowhere differentiable. Please see this, Section 3. For more information, chase the references or google meager nowhere differentiable. – André Nicolas Jul 26 '14 at 02:02
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This phenomenon was touched upon in this previous Answer. – hardmath Jul 26 '14 at 02:13