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 |
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 NERFINISHED ⓘ |
| provides |
classification of functions by asymptotic behavior
ⓘ
rigorous framework for comparing function growth ⓘ |
| relatedTo |
Big-O notation
NERFINISHED
ⓘ
Landau notation NERFINISHED ⓘ Little-o notation NERFINISHED ⓘ asymptotic notation ⓘ hierarchies of functions ⓘ |
| usedFor |
classifying growth of elementary functions
ⓘ
classifying growth of transcendental functions ⓘ comparing divergent series ⓘ comparing infinite sequences ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.