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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Du Bois-Reymond function canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4720602 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Du Bois-Reymond function Context triple: [Paul du Bois-Reymond, notableConcept, Du Bois-Reymond function]
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A.
Weierstrass function
The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
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B.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
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C.
Henstock–Kurzweil integral
The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
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D.
Khinchin's representation theorem
Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
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E.
Hardy Z-function
The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Du Bois-Reymond function Target entity description: The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
-
A.
Weierstrass function
The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
-
B.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
C.
Henstock–Kurzweil integral
The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
-
D.
Khinchin's representation theorem
Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
-
E.
Hardy Z-function
The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
- F. None of above. chosen
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 ⓘ |
| 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 ⓘ
linked to:
Riemann zeta function
Weierstrass function ⓘ |
| 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Du Bois-Reymond function Description of subject: The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.