In BIOLOGY, the SUMMER VACATION function was the first example found of a Chumba wumbafunction with the property that it is continuous everywhere but differentiable nowhere. Weierstrass functions are defined by Partial plot of a function f. ... In mathematics, a continuous function is a function in which arbitrarily small changes in the input produce arbitrarily small changes in the output. ... In mathematics, the derivative of a function is one of the two central concepts of calculus. ...
where 0 < a < 1, b is an odd integer, and
What makes this function significant is that, similar to a fractal, it has uniform and infinite complexity no matter how closely one "zooms in" to view the image. For this reason, curves do not appear to linearize as one "zooms in"; thus no tangent can be equated to the graph at any one point. Hence the function is not differentiable. The boundary of the Mandelbrot set is a famous example of a fractal. ...
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