Du Bois-Reymond theory of orders of infinity
E463064
The Du Bois-Reymond theory of orders of infinity is a foundational framework in analysis that rigorously compares the growth rates of functions by classifying them into hierarchies of infinitesimal and infinite magnitudes.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Du Bois-Reymond theory of orders of infinity canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4720603 — 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 theory of orders of infinity Context triple: [Paul du Bois-Reymond, notableConcept, Du Bois-Reymond theory of orders of infinity]
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A.
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.
-
B.
Problems and Theorems in Analysis (with George Pólya)
"Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
-
C.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
-
D.
Réflexions sur la métaphysique du calcul infinitésimal
Réflexions sur la métaphysique du calcul infinitésimal is a foundational 18th-century treatise by Lazare Carnot that examines the philosophical and logical underpinnings of infinitesimal calculus.
-
E.
Orders of Infinity
"Orders of Infinity" is a mathematical treatise by G. H. Hardy that systematically develops the theory of divergent series and the comparative growth rates of functions in analysis.
- 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 theory of orders of infinity Target entity description: The Du Bois-Reymond theory of orders of infinity is a foundational framework in analysis that rigorously compares the growth rates of functions by classifying them into hierarchies of infinitesimal and infinite magnitudes.
-
A.
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.
-
B.
Problems and Theorems in Analysis (with George Pólya)
"Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
-
C.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
-
D.
Réflexions sur la métaphysique du calcul infinitésimal
Réflexions sur la métaphysique du calcul infinitésimal is a foundational 18th-century treatise by Lazare Carnot that examines the philosophical and logical underpinnings of infinitesimal calculus.
-
E.
Orders of Infinity
"Orders of Infinity" is a mathematical treatise by G. H. Hardy that systematically develops the theory of divergent series and the comparative growth rates of functions in analysis.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
asymptotic growth theory
ⓘ
mathematical theory ⓘ theory in real analysis ⓘ |
| aimsTo |
systematically order different infinitesimals
ⓘ
systematically order different infinities ⓘ |
| appliesTo |
functions defined on the real numbers
ⓘ
real-valued functions ⓘ |
| basedOn |
asymptotic dominance relations between functions
ⓘ
comparisons of ratios of functions ⓘ |
| characterizes |
relative rates of divergence of functions
ⓘ
relative rates of vanishing of functions ⓘ |
| concernsLimitBehavior |
behavior of functions as the variable tends to infinity
ⓘ
behavior of functions as the variable tends to zero ⓘ |
| contributedTo |
foundations of asymptotic analysis
ⓘ
rigorous treatment of infinitesimals and infinities in analysis ⓘ |
| field |
asymptotic analysis
ⓘ
mathematical analysis ⓘ real analysis ⓘ |
| focusesOn |
comparison of growth rates of functions
ⓘ
hierarchies of infinite magnitudes ⓘ hierarchies of infinitesimal magnitudes ⓘ orders of infinity ⓘ orders of smallness ⓘ |
| hasConcept |
higher order infinity
ⓘ
lower order infinity ⓘ scale of infinitesimals ⓘ scale of infinities ⓘ |
| historicalContext | 19th-century analysis ⓘ |
| influenced |
later developments in asymptotic notation
ⓘ
subsequent work on orders of growth in analysis ⓘ |
| mathematicalDomain |
calculus
ⓘ
real variable theory ⓘ theory of functions ⓘ |
| namedAfter | Paul du Bois-Reymond ⓘ |
| provides |
classification of functions by asymptotic behavior
ⓘ
rigorous framework for comparing function growth ⓘ |
| relatedTo |
Big-O notation
ⓘ
Landau notation ⓘ
linked to:
Big-O notation
Little-o notation ⓘ asymptotic notation ⓘ hierarchies of functions ⓘ |
| usedFor |
classifying growth of elementary functions
ⓘ
classifying growth of transcendental functions ⓘ comparing divergent series ⓘ comparing infinite sequences ⓘ |
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Subject: Du Bois-Reymond theory of orders of infinity Description of subject: The Du Bois-Reymond theory of orders of infinity is a foundational framework in analysis that rigorously compares the growth rates of functions by classifying them into hierarchies of infinitesimal and infinite magnitudes.
Referenced by (1)
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