Über den Zahlbegriff¶
Hilbert, D. (1900). Über den Zahlbegriff.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Completeness
- an ordered field is order-complete when every non-empty subset that is bounded above has a least-upper-bound (supremum) in the field (the reals are Dedekind-complete; the rationals are not — Hilbert (1900) elevates this to the Vollständigkeitsaxiom in his axiomatisation of the reals);
This sourceIntroduces the Vollständigkeitsaxiom (axiom of completeness) in Hilbert's axiomatisation of the real numbers: the reals form a system incapable of extension while continuing to satisfy the ordered-field and Archimedean axioms.
- an ordered field is order-complete when every non-empty subset that is bounded above has a least-upper-bound (supremum) in the field (the reals are Dedekind-complete; the rationals are not — Hilbert (1900) elevates this to the Vollständigkeitsaxiom in his axiomatisation of the reals);
Verification¶
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Registry ID ref:ae5eb1ba9f13 · see in the full table