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In mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is also an example of a fractal curve. The Weierstrass function has been historically served the role of a pathological function, being the first published ...
A classic example of a pathology is the Weierstrass function, a function that is continuous everywhere but differentiable nowhere. [1] The sum of a differentiable function and the Weierstrass function is again continuous but nowhere differentiable; so there are at least as many such functions as differentiable functions.
The Cantor function can also be seen as the cumulative probability distribution function of the 1/2-1/2 Bernoulli measure μ supported on the Cantor set: () = ([,]). This probability distribution, called the Cantor distribution, has no discrete part. That is, the corresponding measure is atomless. This is why there are no jump discontinuities ...
A bump function is a smooth function with compact support.. In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives (differentiability class) it has over its domain.
Nowhere differentiable function called also Weierstrass function: continuous everywhere but not differentiable even at a single point. Fast-growing (or rapidly increasing) function; in particular, Ackermann function. Simple function: a real-valued function over a subset of the real line, similar to a step function.
The upshot of Dini's analysis is that a function is differentiable at the point t on the real line (ℝ), only if all the Dini derivatives exist, and have the same value. Sometimes the notation D + f(t) is used instead of f ′ + (t) and D − f(t) is used instead of f ′ (t). [1] Also,
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