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There is a page named "Hilbert's axioms" on Wikipedia
- Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as...16 KB (2,313 words) - 03:58, 9 April 2025
- Euclid's axioms)Euclidean or non-Euclidean. Hilbert's axioms: Hilbert's axioms had the goal of identifying a simple and complete set of independent axioms from which the most...60 KB (7,200 words) - 19:45, 6 July 2025
- Foundations of geometry (section Hilbert's axioms)set of axioms for Euclidean geometry such as Hilbert's axioms or another modern equivalent (Faber 1983, p. 131). Euclid's original set of axioms is ambiguous...76 KB (10,907 words) - 02:44, 15 June 2024
- geometrical axioms. ... On the other hand a direct method is needed for the proof of the compatibility of the arithmetical axioms." Hilbert's statement...15 KB (1,500 words) - 01:07, 19 March 2024
- Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed...9 KB (1,158 words) - 13:50, 18 August 2024
- Finite dimensional Hilbert spaces)rather easy to prove that all definitions of Euclidean spaces satisfy Hilbert's axioms, and that those involving real numbers (including the above given definition)...47 KB (6,967 words) - 08:16, 28 June 2025
satisfy the Wightman axioms. Haag–Kastler axioms Hilbert's sixth problem Axiomatic quantum field theory Local quantum field theory "Hilbert's sixth problem"...19 KB (2,719 words) - 22:48, 18 July 2025 - axioms, Pasch's axiom can be proved as a theorem; it is a consequence of the plane separation axiom when that is taken as one of the axioms. Hilbert uses...8 KB (1,008 words) - 15:16, 20 March 2025
- Zermelo-Fraenkel axioms)the axioms of Zermelo–Fraenkel set theory. Most of the axioms state the existence of particular sets defined from other sets. For example, the axiom of...46 KB (6,270 words) - 22:21, 15 July 2025
- Hilbert plane)basis of Euclidean geometry, so other systems (such as Hilbert's axioms without the parallel axiom) are used instead. In Euclid's Elements, the first 28...8 KB (1,057 words) - 07:07, 15 February 2025
Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several...41 KB (3,685 words) - 16:03, 1 July 2025 - used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge...14 KB (1,544 words) - 15:50, 16 July 2025
- universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.[additional...92 KB (12,173 words) - 02:29, 24 June 2025
- mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...49 KB (6,478 words) - 03:13, 3 April 2025
- Profile at University of St. Andrews Hilbert Bernays Project Hilbert's 23 Problems Address Hilbert's Program Hilberts radio speech recorded in Königsberg
- are really due to the Italians. Hilbert's chief contribution to the foundations of geometry is his study of the axioms needed for the proof of particular
- the axioms do, in fact, hold in your system. Unnecessary axioms increase the work load for this with no added benefit. Aside: to show that an axiom is