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Axiom

An axiom, postulate, or assumption, is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.

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Etymology

Historical development

Mathematical logic

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Axiom

Nodes170
Edges169
Triples81
Avg. degree1.99
Density0.011765
Components1

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Axiom

Top relations

related to Further reading · 16
Axiom → Axioms, Belmont, Brooks, California, CS1, Elliot, Evolutionist Theory, Introduction, ISBN, John Cook Wilson, Mendelson, October, On, Oxford, Wadsworth, Wikidata Q26720682
related to Early Greeks · 11
Axiom → All, Aristotle, Aristotle's Posterior Analytics, As, Axioms, Euclid, Greeks, However, Tautologies, The, They
related to Modern development · 11
Axiom → Alessandro Padoa, As, Euclid, Euclid's, Giuseppe Peano, However, Mario Pieri, One, Structuralist, Such, The
related to Other sciences · 11
Axiom → As, Darwin's Natural, Einstein's, Experimental, For, If, In, Maxwell's, Mendel's, Newton's, These
related to Further discussion · 6
Axiom → Boolean, Early, Galois, In, The, Ultimately
related to Non-logical axioms · 5
Axiom → Almost, Another, Non-logical, Reasoning, Thus
related to Etymology · 4
Axiom → Among, Euclid, Greek, The
is a · 3
Axiom → premise or starting point for reasoning.In mathematics, statement that is so evident or well-established, statement that serves as a starting point from which other statements are logically derived
related to External links · 3
Axiom → Metamath, PhilPapersAxiom, PlanetMath
see also · 3
Axiom → Axiomatic, JurisTheoremPresuppositionPrinciple, Mathematics

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Important terminology

axioms set theory mathematical one displaystyle postulates mathematics non-logical logic system logical geometry postulate modern true also arithmetic phi example

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Axiomis astatement that is so evident or well-established0.90text
Axiomis apremise or starting point for reasoning.In mathematics0.90text
Axiomis astatement that serves as a starting point from which other statements are logically derived0.90text
entanglementinstance ofIt was created so as to try to give deterministic explanation to phenomena0.80text
the universe itselfinstance ofwhat happens in a completely closed quantum system0.80text
etcinstance ofwhat happens in a completely closed quantum system0.80text
Morseinstance ofSometimes slightly stronger theories0.80text
Boolean algebra made elaborate efforts to derive them from traditional arithmeticinstance ofThe idea that alternative mathematical systems might exist was very troubling to mathematicians of the 19th century and the developers of systems0.80text
Axiomrelated to Early GreeksThe0.60section
Axiomrelated to Early GreeksGreeks0.60section
Axiomrelated to Early GreeksTautologies0.60section
Axiomrelated to Early GreeksAxioms0.60section

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    Min side: 3
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