Stetigkeit und irrationale Zahlen
E634838
"Stetigkeit und irrationale Zahlen" is Richard Dedekind’s seminal 1872 work in which he rigorously defines real numbers and continuity via Dedekind cuts, laying a foundation for modern analysis.
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical treatise ⓘ work on real analysis ⓘ |
| author | Richard Dedekind NERFINISHED ⓘ |
| authorBelongsToSchool | arithmetization of analysis ⓘ |
| contribution |
first rigorous definition of real numbers via cuts
ⓘ
formalization of continuity using order completeness ⓘ |
| countryOfOrigin | Germany ⓘ |
| defines |
irrational number
ⓘ
real number ⓘ |
| field |
mathematical analysis
ⓘ
mathematics ⓘ number theory ⓘ |
| focusesOn |
logical foundations of continuity
ⓘ
rigorous construction of the real numbers ⓘ |
| hasForm | essay ⓘ |
| historicalPeriod | 19th-century mathematics ⓘ |
| importance |
foundational work in the theory of real numbers
ⓘ
seminal text in modern analysis ⓘ |
| influenced |
axiomatic treatment of real numbers
ⓘ
foundations of mathematics ⓘ modern real analysis ⓘ |
| introducesConcept | Dedekind cut NERFINISHED ⓘ |
| keyConcept |
completeness of the real line
ⓘ
continuity of the number line ⓘ cut in the rational numbers ⓘ partition of the rational numbers ⓘ |
| language | German ⓘ |
| mainSubject |
Dedekind cuts
NERFINISHED
ⓘ
continuity ⓘ foundations of analysis ⓘ real numbers ⓘ |
| originalTitle | Stetigkeit und irrationale Zahlen ⓘ |
| publicationYear | 1872 ⓘ |
| publisherType | mathematical journal or proceedings ⓘ |
| relatedConcept |
completeness axiom
ⓘ
least upper bound property ⓘ real number line ⓘ |
| relatedWork | Was sind und was sollen die Zahlen? NERFINISHED ⓘ |
| timeRequiredForDevelopment | late 19th century formalization of analysis ⓘ |
| usesMethod |
order-theoretic approach
ⓘ
set-theoretic construction ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.