Du Bois-Reymond function
E463063
continuous function
mathematical function
nowhere differentiable function
pathological function in analysis
real-valued function
The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
Statements (35)
| Predicate | Object |
|---|---|
| instanceOf |
continuous function
ⓘ
mathematical function ⓘ nowhere differentiable function ⓘ pathological function in analysis ⓘ real-valued function ⓘ |
| appearsIn |
courses on advanced calculus
ⓘ
courses on measure and integration ⓘ literature on pathological examples in analysis ⓘ |
| clarification | distinct from the Du Bois-Reymond antiderivative construction in the theory of functions ⓘ |
| codomain | real numbers ⓘ |
| domain | real numbers ⓘ |
| field | real analysis ⓘ |
| historicalRole | one of the earliest explicit examples of a continuous nowhere differentiable function ⓘ |
| mathematicalClassification |
example of a function that is continuous but nowhere monotone on any interval (in typical constructions)
ⓘ
example of a function with extreme irregularity ⓘ |
| namedAfter | Paul du Bois-Reymond NERFINISHED ⓘ |
| property |
constructed as an infinite series
ⓘ
continuous everywhere ⓘ differentiable nowhere ⓘ not representable as a power series around any point ⓘ provides counterexample to the belief that most continuous functions are differentiable ⓘ uniform limit of continuous functions ⓘ |
| relatedTo |
Brownian motion sample paths
ⓘ
Riemann function NERFINISHED ⓘ Weierstrass function NERFINISHED ⓘ |
| roleInEducation |
helps demonstrate limitations of geometric intuition about smooth curves
ⓘ
used to illustrate the difference between continuity and differentiability ⓘ used to motivate precise definitions of differentiability ⓘ |
| topic |
nowhere differentiable functions
ⓘ
pointwise convergence of series of functions ⓘ regularity of functions ⓘ uniform convergence of series of functions ⓘ |
| usedAs |
counterexample in differentiability theory
ⓘ
illustration of pathological behavior of continuous functions ⓘ standard example in real analysis textbooks ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.