Seven Funky Functions
It turns out that the Weierstrass function is far from being an isolated example: although it is "pathological", it is also "typical" of continuous functions. In a topological sense, it can be shown that the set of nowhere-differentiable real-valued functions on [0, 1] is dense in the vector space C([0, 1]; R) of all continuous real-valued functions on [0, 1] with the topology of uniform convergence. |
The Maple Worksheets above prepared by Prof. Girardi. Unless otherwise stated, Maple Code in these Maple Worksheets were prepared by Prof. Girardi.