Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Theorem> ?p ?o }
- Theorem abstract "In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems—and generally accepted statements, such as axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific theory, which is empirical.Many mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called hypotheses or premises. In light of the interpretation of proof as justification of truth, the conclusion is often viewed as a necessary consequence of the hypotheses, namely, that the conclusion is true in case the hypotheses are true, without any further assumptions. However, the conditional could be interpreted differently in certain deductive systems, depending on the meanings assigned to the derivation rules and the conditional symbol.Although they can be written in a completely symbolic form, for example, within the propositional calculus, theorems are often expressed in a natural language such as English. The same is true of proofs, which are often expressed as logically organized and clearly worded informal arguments, intended to convince readers of the truth of the statement of the theorem beyond any doubt, and from which a formal symbolic proof can in principle be constructed. Such arguments are typically easier to check than purely symbolic ones—indeed, many mathematicians would express a preference for a proof that not only demonstrates the validity of a theorem, but also explains in some way why it is obviously true. In some cases, a picture alone may be sufficient to prove a theorem. Because theorems lie at the core of mathematics, they are also central to its aesthetics. Theorems are often described as being \"trivial\", or \"difficult\", or \"deep\", or even \"beautiful\". These subjective judgments vary not only from person to person, but also with time: for example, as a proof is simplified or better understood, a theorem that was once difficult may become trivial. On the other hand, a deep theorem may be simply stated, but its proof may involve surprising and subtle connections between disparate areas of mathematics. Fermat's Last Theorem is a particularly well-known example of such a theorem.".
- Theorem thumbnail Pythagorean_Proof_(3).PNG?width=300.
- Theorem wikiPageExternalLink www.theoremoftheday.org.
- Theorem wikiPageID "30977".
- Theorem wikiPageLength "27340".
- Theorem wikiPageOutDegree "138".
- Theorem wikiPageRevisionID "706531218".
- Theorem wikiPageWikiLink Alfréd_Rényi.
- Theorem wikiPageWikiLink Aphorism.
- Theorem wikiPageWikiLink Axiom.
- Theorem wikiPageWikiLink Banach–Tarski_paradox.
- Theorem wikiPageWikiLink Bayes_rule.
- Theorem wikiPageWikiLink Belief.
- Theorem wikiPageWikiLink Brute-force_search.
- Theorem wikiPageWikiLink Bxc3xa9zouts_identity.
- Theorem wikiPageWikiLink Category:Logical_consequence.
- Theorem wikiPageWikiLink Category:Logical_expressions.
- Theorem wikiPageWikiLink Category:Mathematical_proofs.
- Theorem wikiPageWikiLink Category:Mathematical_terminology.
- Theorem wikiPageWikiLink Category:Statements.
- Theorem wikiPageWikiLink Category:Theorems.
- Theorem wikiPageWikiLink Classification_of_finite_simple_groups.
- Theorem wikiPageWikiLink Collatz_conjecture.
- Theorem wikiPageWikiLink Combinatorics.
- Theorem wikiPageWikiLink Completeness_(logic).
- Theorem wikiPageWikiLink Conjecture.
- Theorem wikiPageWikiLink Converse_(logic).
- Theorem wikiPageWikiLink Corollary.
- Theorem wikiPageWikiLink Cramers_rule.
- Theorem wikiPageWikiLink Deductive_reasoning.
- Theorem wikiPageWikiLink Definition.
- Theorem wikiPageWikiLink Doron_Zeilberger.
- Theorem wikiPageWikiLink Douglas_Hofstadter.
- Theorem wikiPageWikiLink Epistemology.
- Theorem wikiPageWikiLink Erdős_number.
- Theorem wikiPageWikiLink Euclidean_division.
- Theorem wikiPageWikiLink Eulers_formula.
- Theorem wikiPageWikiLink Experiment.
- Theorem wikiPageWikiLink Exponential_function.
- Theorem wikiPageWikiLink Falsifiability.
- Theorem wikiPageWikiLink Fermats_Last_Theorem.
- Theorem wikiPageWikiLink File:CollatzFractal.png.
- Theorem wikiPageWikiLink First-order_logic.
- Theorem wikiPageWikiLink Formal_language.
- Theorem wikiPageWikiLink Formal_proof.
- Theorem wikiPageWikiLink Formal_system.
- Theorem wikiPageWikiLink Formula.
- Theorem wikiPageWikiLink Four_color_theorem.
- Theorem wikiPageWikiLink Fundamental_lemma_(Langlands_program).
- Theorem wikiPageWikiLink Gausss_lemma_(polynomial).
- Theorem wikiPageWikiLink Generalization.
- Theorem wikiPageWikiLink Goldbachs_conjecture.
- Theorem wikiPageWikiLink Googol.
- Theorem wikiPageWikiLink Group_theory.
- Theorem wikiPageWikiLink Gödel,_Escher,_Bach.
- Theorem wikiPageWikiLink Harnacks_principle.
- Theorem wikiPageWikiLink Hypothesis.
- Theorem wikiPageWikiLink Identity_(mathematics).
- Theorem wikiPageWikiLink Indicative_conditional.
- Theorem wikiPageWikiLink Inference.
- Theorem wikiPageWikiLink Interpretation_(logic).
- Theorem wikiPageWikiLink Kepler_conjecture.
- Theorem wikiPageWikiLink Kolmogorovs_zeroxe2x80x93one_law.
- Theorem wikiPageWikiLink Lambda_calculus.
- Theorem wikiPageWikiLink Law_of_cosines.
- Theorem wikiPageWikiLink Law_of_large_numbers.
- Theorem wikiPageWikiLink Laws_of_science.
- Theorem wikiPageWikiLink Least-upper-bound_property.
- Theorem wikiPageWikiLink Lemma_(mathematics).
- Theorem wikiPageWikiLink List_of_theorems.
- Theorem wikiPageWikiLink Logic.
- Theorem wikiPageWikiLink Logical_consequence.
- Theorem wikiPageWikiLink Macro_(computer_science).
- Theorem wikiPageWikiLink Mathematical_proof.
- Theorem wikiPageWikiLink Mathematics.
- Theorem wikiPageWikiLink Measure_(mathematics).
- Theorem wikiPageWikiLink Mertens_conjecture.
- Theorem wikiPageWikiLink Metamath.
- Theorem wikiPageWikiLink Metatheorem.
- Theorem wikiPageWikiLink Modal_logic.
- Theorem wikiPageWikiLink Natural_number.
- Theorem wikiPageWikiLink Nonsense.
- Theorem wikiPageWikiLink Number_theory.
- Theorem wikiPageWikiLink Paradox.
- Theorem wikiPageWikiLink Parameter.
- Theorem wikiPageWikiLink Paul_Erdős.
- Theorem wikiPageWikiLink Paul_Halmos.
- Theorem wikiPageWikiLink Pigeonhole_principle.
- Theorem wikiPageWikiLink Pons_asinorum.
- Theorem wikiPageWikiLink Premise.
- Theorem wikiPageWikiLink Principle.
- Theorem wikiPageWikiLink Proof_theory.
- Theorem wikiPageWikiLink Proposition.
- Theorem wikiPageWikiLink Propositional_calculus.
- Theorem wikiPageWikiLink Pythagorean_theorem.
- Theorem wikiPageWikiLink Q.E.D..
- Theorem wikiPageWikiLink Q:Paul_Erdős.
- Theorem wikiPageWikiLink Quadratic_reciprocity.
- Theorem wikiPageWikiLink Rectangle.
- Theorem wikiPageWikiLink Rewriting.