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Axiomatic system

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Axiomatische methode

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axiomatic system

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(logic) A set of axioms from which theorems can be derived.

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axiomatische methode

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set of axioms from which some or all axioms can be used in conjunction to logically derive theorems
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" Every axiomatic system will contain truths... "
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„Even in closed axiomatic systems, not all propositions are decidable.
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To Turing's amazement, Petros also wasn't too clear about the Peano-Dedekind axiomatic system.
Let niet op hemLiterature Literature
Its first application is to the very basis of arithmetic, the Peano-Dedekind axiomatic system.’
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I was talking about the internal limits of axiomatic systems.”
Een helaas nog steeds gebrekkige internemarkt zorgt voor een gebrekkige Europese concurrentiekracht.Literature Literature
“But we don’t know what kind of axiomatic system the complex logic is based on in this case,” Fisher replied.
Niemand kan opstaan uit de doodLiterature Literature
In 1922 and 1925, he published two papers that sought to improve Zermelo's axiomatic system; the result is the Zermelo–Fraenkel axioms.
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Absolute geometry is an incomplete axiomatic system, in the sense that one can add extra independent axioms without making the axiom system inconsistent.
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For example, Euclidean geometry is an axiomatic system, in which all theorems ("true statements given the axioms") are derived from a finite number of axioms.
Hij vond geen enkele versnellerWikiMatrix WikiMatrix
Starting with Moritz Pasch in 1882, many improved axiomatic systems for geometry have been proposed, the best known being those of Hilbert, George Birkhoff, and Tarski.
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Concerns that mathematics had not been built on a proper foundation led to the development of axiomatic systems for fundamental areas of mathematics such as arithmetic, analysis, and geometry.
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Thus, in order to show that any axiomatic system of mathematics is in fact consistent, one needs to first assume the consistency of a system of mathematics that is in a sense stronger than the system to be proven consistent.
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In this sense, Euclidean geometry is more concrete than many modern axiomatic systems such as set theory, which often assert the existence of objects without saying how to construct them, or even assert the existence of objects that cannot be constructed within the theory.
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In that article, he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g., the Peano axioms or Zermelo–Fraenkel set theory with the axiom of choice), that: If a (logical or axiomatic formal) system is consistent, it cannot be complete.
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No generalization can hold generally without an airtight system of axiomatics to begin with.
Het klinkt heel mooiLiterature Literature
The modular representation theory entered a new era as the techniques of the classification were axiomatized, including fusion systems, Luis Puig's theory of pairs and nilpotent blocks.
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Euclidean geometry is an axiomatic system, in which all theorems ("true statements") are derived from a small number of simple axioms.
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Zermelo began to axiomatize set theory in 1905; in 1908, he published his results despite his failure to prove the consistency of his axiomatic system.
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Starting with Moritz Pasch in 1882, many improved axiomatic systems for geometry have been proposed, the best known being those of Hilbert,[35] George Birkhoff,[36] and Tarski.[37]
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If a (logical or axiomatic formal) system is consistent, it cannot be complete.
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In that article, he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g., the Peano axioms or Zermelo–Fraenkel set theory with the axiom of choice), that:
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The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms.
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In mathematics, Zermelo–Fraenkel set theory with the axiom of choice, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets without the paradoxes of naive set theory like Russell’s paradox.
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But in the context of a common market, in which it is axiomatic that trade should not be distorted by peculiarities of the respective fiscal systems, such a method of calculating excise duty raises severe difficulties.
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"ZFC" redirects here. For other uses, see ZFC (disambiguation). In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets free of paradoxes such as Russell's paradox.
Bij de Verordeningen (EG) nr. #/# en (EG) nr. #/# van de Commissie zijn de bepalingen voor de uitvoering van de tweede fase van het werkprogramma zoals bedoeld in artikel #, lid #, van Richtlijn #/#/EEG, vastgesteld en is een lijst opgesteld van werkzame stoffen die moeten worden beoordeeld met het oog op hun eventuele opneming in bijlage I bij Richtlijn #/#/EEGParaCrawl Corpus ParaCrawl Corpus
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