KnowraHilbert's axiomsLinked fromLinked fromThe 7 pages that link to Hilbert's axioms, each with the reason it gives.All 7Broader topic 2Related 1Narrower topic 2Compared with 2AxiomBroader topic: They illustrate the modern effort to state assumptions explicitly and examine their relations.Foundations of GeometryBroader topic: Hilbert made implicit assumptions in classical geometry explicit and systematically organized.BetweennessNarrower topic: Hilbert’s system gives betweenness its own axioms alongside incidence and congruence.Pasch's axiomNarrower topic: Pasch's axiom belongs to the order assumptions in Hilbert's formalization.Tarski's axiomsCompared with: Unlike Tarski's system, Hilbert's takes lines and planes as primitive objects.Cantor–Dedekind axiomCompared with: Hilbert’s approach axiomatizes geometric structure rather than identifying line points directly with real numbers.Pasch's theoremRelated: Hilbert's order axioms include a formal version of the line-crossing principle.