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- Mathematical_fallacy abstract "In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules.The traditional way of presenting a mathematical fallacy is to give an invalid step of deduction mixed in with valid steps, so that the meaning of fallacy is here slightly different from the logical fallacy. The latter applies normally to a form of argument that is not a genuine rule of logic, where the problematic mathematical step is typically a correct rule applied with a tacit wrong assumption. Beyond pedagogy, the resolution of a fallacy can lead to deeper insights into a subject (such as the introduction of Pasch's axiom of Euclidean geometry). Pseudaria, an ancient lost book of false proofs, is attributed to Euclid.Mathematical fallacies exist in many branches of mathematics. In elementary algebra, typical examples may involve a step where division by zero is performed, where a root is incorrectly extracted or, more generally, where different values of a multiple valued function are equated. Well-known fallacies also exist in elementary Euclidean geometry and calculus.".
- Mathematical_fallacy wikiPageExternalLink books?id=M6DvzoKlcicC.
- Mathematical_fallacy wikiPageExternalLink books?id=ugrXqDEyPU8C.
- Mathematical_fallacy wikiPageExternalLink books?id=zNvvoFEzP8IC&printsec=frontcover.
- Mathematical_fallacy wikiPageExternalLink math_jokes.html.
- Mathematical_fallacy wikiPageExternalLink index.shtml.
- Mathematical_fallacy wikiPageExternalLink 49-Math-Jokes.
- Mathematical_fallacy wikiPageExternalLink falseProofs.
- Mathematical_fallacy wikiPageID "254364".
- Mathematical_fallacy wikiPageRevisionID "606677277".
- Mathematical_fallacy hasPhotoCollection Mathematical_fallacy.
- Mathematical_fallacy subject Category:Humour.
- Mathematical_fallacy subject Category:Logical_fallacies.
- Mathematical_fallacy subject Category:Mathematical_proofs.
- Mathematical_fallacy subject Category:Proof_theory.
- Mathematical_fallacy type Abstraction100002137.
- Mathematical_fallacy type Argument106648724.
- Mathematical_fallacy type Cognition100023271.
- Mathematical_fallacy type Communication100033020.
- Mathematical_fallacy type Content105809192.
- Mathematical_fallacy type Evidence106643408.
- Mathematical_fallacy type Fallacy105893916.
- Mathematical_fallacy type Idea105833840.
- Mathematical_fallacy type Indication106797169.
- Mathematical_fallacy type LogicalFallacies.
- Mathematical_fallacy type LogicalFallacy105894143.
- Mathematical_fallacy type MathematicalProof106647864.
- Mathematical_fallacy type MathematicalProofs.
- Mathematical_fallacy type Misconception105893653.
- Mathematical_fallacy type Proof106647614.
- Mathematical_fallacy type PsychologicalFeature100023100.
- Mathematical_fallacy comment "In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof.".
- Mathematical_fallacy label "Demostración inválida".
- Mathematical_fallacy label "Mathematical fallacy".
- Mathematical_fallacy label "Prova inválida".
- Mathematical_fallacy label "Pseudo-démonstration d'égalité entre nombres".
- Mathematical_fallacy label "Sofisma algebrico".
- Mathematical_fallacy label "إثبات خاطئ".
- Mathematical_fallacy label "無效證明".
- Mathematical_fallacy sameAs Demostración_inválida.
- Mathematical_fallacy sameAs Pseudo-démonstration_d'égalité_entre_nombres.
- Mathematical_fallacy sameAs Sofisma_algebrico.
- Mathematical_fallacy sameAs Prova_inválida.
- Mathematical_fallacy sameAs m.01lqjn.
- Mathematical_fallacy sameAs Q387855.
- Mathematical_fallacy sameAs Q387855.
- Mathematical_fallacy sameAs Mathematical_fallacy.
- Mathematical_fallacy wasDerivedFrom Mathematical_fallacy?oldid=606677277.
- Mathematical_fallacy isPrimaryTopicOf Mathematical_fallacy.