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- Axiom abstract "An axiom or postulate as defined in classic philosophy, is a statement (in mathematics often shown in symbolic form) that is so evident or well-established, that it is accepted without controversy or question. Thus, the axiom can be used as the premise or starting point for further reasoning or arguments, usually in logic or in mathematicsThe word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'As used in modern logic, an axiom is simply a premise or starting point for reasoning. Whether it is meaningful (and, if so, what it means) for an axiom, or any mathematical statement, to be \"true\" is a central question in the philosophy of mathematics, with modern mathematicians holding a multitude of different opinions.As used in mathematics, the term axiom is used in two related but distinguishable senses: \"logical axioms\" and \"non-logical axioms\". Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, \"axiom\", \"postulate\", and \"assumption\" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. As modern mathematics admits multiple, equally \"true\" systems of logic, precisely the same thing must be said for logical axioms - they both define and are specific to the particular system of logic that is being invoked. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Within the system they define, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow otherwise they would be classified as theorems. However, an axiom in one system may be a theorem in another, and vice versa.".
- Axiom wikiPageExternalLink axioms.
- Axiom wikiPageID "928".
- Axiom wikiPageLength "31485".
- Axiom wikiPageOutDegree "180".
- Axiom wikiPageRevisionID "698894917".
- Axiom wikiPageWikiLink Abstract_algebra.
- Axiom wikiPageWikiLink Alain_Aspect.
- Axiom wikiPageWikiLink Albert_Einstein.
- Axiom wikiPageWikiLink Alessandro_Padoa.
- Axiom wikiPageWikiLink Algebraic_topology.
- Axiom wikiPageWikiLink Ancient_Greece.
- Axiom wikiPageWikiLink Ancient_philosophy.
- Axiom wikiPageWikiLink Angle.
- Axiom wikiPageWikiLink Angles.
- Axiom wikiPageWikiLink Aristotle.
- Axiom wikiPageWikiLink Arithmetic.
- Axiom wikiPageWikiLink Axiom_schema.
- Axiom wikiPageWikiLink Axiomatic_geometry.
- Axiom wikiPageWikiLink Axiomatic_system.
- Axiom wikiPageWikiLink Bells_theorem.
- Axiom wikiPageWikiLink Bertrand_Russell.
- Axiom wikiPageWikiLink Boethius.
- Axiom wikiPageWikiLink Boolean_algebra.
- Axiom wikiPageWikiLink Category:Concepts_in_logic.
- Axiom wikiPageWikiLink Category:Formal_systems.
- Axiom wikiPageWikiLink Category:Mathematical_axioms.
- Axiom wikiPageWikiLink Category:Mathematical_terminology.
- Axiom wikiPageWikiLink Change_of_variables.
- Axiom wikiPageWikiLink Circle.
- Axiom wikiPageWikiLink Class_(set_theory).
- Axiom wikiPageWikiLink Combinatorics.
- Axiom wikiPageWikiLink Commutative_property.
- Axiom wikiPageWikiLink Complex_analysis.
- Axiom wikiPageWikiLink Conservative_extension.
- Axiom wikiPageWikiLink Consistency.
- Axiom wikiPageWikiLink Continuum_hypothesis.
- Axiom wikiPageWikiLink Copenhagen_interpretation.
- Axiom wikiPageWikiLink Corollary.
- Axiom wikiPageWikiLink David_Hilbert.
- Axiom wikiPageWikiLink Deductive_reasoning.
- Axiom wikiPageWikiLink Determinism.
- Axiom wikiPageWikiLink Differential_geometry.
- Axiom wikiPageWikiLink Differential_topology.
- Axiom wikiPageWikiLink Discourse.
- Axiom wikiPageWikiLink Dogma.
- Axiom wikiPageWikiLink EPR_paradox.
- Axiom wikiPageWikiLink Elliptic_geometry.
- Axiom wikiPageWikiLink Ergodic_theory.
- Axiom wikiPageWikiLink Euclid.
- Axiom wikiPageWikiLink Euclidean_geometry.
- Axiom wikiPageWikiLink Euclids_Elements.
- Axiom wikiPageWikiLink Falsifiability.
- Axiom wikiPageWikiLink Field_(mathematics).
- Axiom wikiPageWikiLink First-order_logic.
- Axiom wikiPageWikiLink Forcing_(mathematics).
- Axiom wikiPageWikiLink Formal_language.
- Axiom wikiPageWikiLink Formal_system.
- Axiom wikiPageWikiLink Free_variables_and_bound_variables.
- Axiom wikiPageWikiLink Galois_theory.
- Axiom wikiPageWikiLink Geminus.
- Axiom wikiPageWikiLink General_relativity.
- Axiom wikiPageWikiLink General_topology.
- Axiom wikiPageWikiLink Geometry.
- Axiom wikiPageWikiLink Georg_Cantor.
- Axiom wikiPageWikiLink Giuseppe_Peano.
- Axiom wikiPageWikiLink Gottlob_Frege.
- Axiom wikiPageWikiLink Greek_language.
- Axiom wikiPageWikiLink Grothendieck_universe.
- Axiom wikiPageWikiLink Group_(mathematics).
- Axiom wikiPageWikiLink Group_theory.
- Axiom wikiPageWikiLink Gxc3xb6dels_completeness_theorem.
- Axiom wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Axiom wikiPageWikiLink Henri_Poincaré.
- Axiom wikiPageWikiLink Homology_(mathematics).
- Axiom wikiPageWikiLink Homotopy.
- Axiom wikiPageWikiLink Hyperbolic_geometry.
- Axiom wikiPageWikiLink Inaccessible_cardinal.
- Axiom wikiPageWikiLink Infinity.
- Axiom wikiPageWikiLink Integer.
- Axiom wikiPageWikiLink Isaac_Newton.
- Axiom wikiPageWikiLink Isomorphism.
- Axiom wikiPageWikiLink John_Stewart_Bell.
- Axiom wikiPageWikiLink Kurt_Gödel.
- Axiom wikiPageWikiLink Line_(geometry).
- Axiom wikiPageWikiLink Line–line_intersection.
- Axiom wikiPageWikiLink List_of_axioms.
- Axiom wikiPageWikiLink Logic.
- Axiom wikiPageWikiLink Logical_connective.
- Axiom wikiPageWikiLink Logical_consequence.
- Axiom wikiPageWikiLink Logical_truth.
- Axiom wikiPageWikiLink Löwenheim–Skolem_theorem.
- Axiom wikiPageWikiLink Mario_Pieri.
- Axiom wikiPageWikiLink Mathematical_logic.
- Axiom wikiPageWikiLink Mathematical_proof.
- Axiom wikiPageWikiLink Mathematical_theory.
- Axiom wikiPageWikiLink Mathematician.
- Axiom wikiPageWikiLink Mathematics.
- Axiom wikiPageWikiLink Measure_(mathematics).
- Axiom wikiPageWikiLink Model_theory.