Was sind und was sollen die Zahlen?¶
Dedekind, R. (1888). Was sind und was sollen die Zahlen?.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Equivalence Relation
- … crystallises with the development of set theory and abstract algebra in the late nineteenth and early twentieth centuries (Dedekind's Was sind und was sollen die Zahlen? of 1888; Frege's Grundgesetze der Arithmetik; Russell's Principles of Mathematics; van der Waerden's Moderne Algebra of 1930-1931).
This sourceFoundational set-theoretic construction of the natural numbers; explicitly notes the similarity relation is reflexive, symmetric, and transitive (an equivalence relation) and works with its equivalence classes. Cited in prose (Notes) on the late-19th-century crystallization of the three-axiom characterization; no FACT marker.
- … crystallises with the development of set theory and abstract algebra in the late nineteenth and early twentieth centuries (Dedekind's Was sind und was sollen die Zahlen? of 1888; Frege's Grundgesetze der Arithmetik; Russell's Principles of Mathematics; van der Waerden's Moderne Algebra of 1930-1931).
- Infinity
- and (1888) on Peano arithmetic precursors
This sourceFoundational set-theoretic treatment of equivalence relations and quotient constructions in the development of the natural-number concept; the explicit axiomatic three-property characterisation (reflexivity, symmetry, transitivity) is consolidated in this and subsequent late-nineteenth-century foundational works.
- and (1888) on Peano arithmetic precursors
- Mathematical Induction
- Dedekind
This sourceFoundational set-theoretic treatment of equivalence relations and quotient constructions in the development of the natural-number concept; the explicit axiomatic three-property characterisation (reflexivity, symmetry, transitivity) is consolidated in this and subsequent late-nineteenth-century foundational works.
- Dedekind
- Order
- formalized the natural-number order through his chain construction
This sourceFoundational set-theoretic treatment of equivalence relations and quotient constructions in the development of the natural-number concept; the explicit axiomatic three-property characterisation (reflexivity, symmetry, transitivity) is consolidated in this and subsequent late-nineteenth-century foundational works.
- formalized the natural-number order through his chain construction
- Relation
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