Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Mathematical_fallacy> ?p ?o }
- 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 and the five color theorem of graph theory). 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.
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- Mathematical_fallacy wikiPageExternalLink 49-Math-Jokes.
- Mathematical_fallacy wikiPageExternalLink falseProofs.
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- Mathematical_fallacy wikiPageWikiLink All_horses_are_the_same_color.
- Mathematical_fallacy wikiPageWikiLink All_horses_are_the_same_colour.
- Mathematical_fallacy wikiPageWikiLink Anomalous_cancellation.
- Mathematical_fallacy wikiPageWikiLink Bisection.
- Mathematical_fallacy wikiPageWikiLink Calculus.
- Mathematical_fallacy wikiPageWikiLink Cambridge_University_Press.
- Mathematical_fallacy wikiPageWikiLink Category:Humour.
- Mathematical_fallacy wikiPageWikiLink Category:Logical_fallacies.
- Mathematical_fallacy wikiPageWikiLink Category:Mathematical_proofs.
- Mathematical_fallacy wikiPageWikiLink Category:Proof_theory.
- Mathematical_fallacy wikiPageWikiLink Congruence_(geometry).
- Mathematical_fallacy wikiPageWikiLink Contradiction.
- Mathematical_fallacy wikiPageWikiLink Cut-the-Knot.
- Mathematical_fallacy wikiPageWikiLink Cut-the-knot.
- Mathematical_fallacy wikiPageWikiLink Difference_of_squares.
- Mathematical_fallacy wikiPageWikiLink Difference_of_two_squares.
- Mathematical_fallacy wikiPageWikiLink Differential_(mathematics).
- Mathematical_fallacy wikiPageWikiLink Division_by_zero.
- Mathematical_fallacy wikiPageWikiLink Dover_Publications.
- Mathematical_fallacy wikiPageWikiLink Elementary_algebra.
- Mathematical_fallacy wikiPageWikiLink Euclid.
- Mathematical_fallacy wikiPageWikiLink Euclidean_geometry.
- Mathematical_fallacy wikiPageWikiLink Exponentiation.
- Mathematical_fallacy wikiPageWikiLink Factorization.
- Mathematical_fallacy wikiPageWikiLink Fallacy.
- Mathematical_fallacy wikiPageWikiLink Five_color_theorem.
- Mathematical_fallacy wikiPageWikiLink Geometry.
- Mathematical_fallacy wikiPageWikiLink Graph_theory.
- Mathematical_fallacy wikiPageWikiLink Howler_(error).
- Mathematical_fallacy wikiPageWikiLink Imaginary_unit.
- Mathematical_fallacy wikiPageWikiLink Informal_fallacy.
- Mathematical_fallacy wikiPageWikiLink Integral.
- Mathematical_fallacy wikiPageWikiLink Integration_by_parts.
- Mathematical_fallacy wikiPageWikiLink Inverse_function.
- Mathematical_fallacy wikiPageWikiLink Isosceles_triangle.
- Mathematical_fallacy wikiPageWikiLink Lewis_Carroll.
- Mathematical_fallacy wikiPageWikiLink Limit_of_a_function.
- Mathematical_fallacy wikiPageWikiLink List_of_incomplete_proofs.
- Mathematical_fallacy wikiPageWikiLink Mathematical_Association_of_America.
- Mathematical_fallacy wikiPageWikiLink Mathematical_induction.
- Mathematical_fallacy wikiPageWikiLink Mathematical_proof.
- Mathematical_fallacy wikiPageWikiLink Mathematics.
- Mathematical_fallacy wikiPageWikiLink Multiple_valued_function.
- Mathematical_fallacy wikiPageWikiLink Multivalued_function.
- Mathematical_fallacy wikiPageWikiLink Nth_root.
- Mathematical_fallacy wikiPageWikiLink Paradox.
- Mathematical_fallacy wikiPageWikiLink Paschs_axiom.
- Mathematical_fallacy wikiPageWikiLink Polynomial_greatest_common_divisor.
- Mathematical_fallacy wikiPageWikiLink Principal_value.
- Mathematical_fallacy wikiPageWikiLink Proof_by_induction.
- Mathematical_fallacy wikiPageWikiLink Proof_by_intimidation.
- Mathematical_fallacy wikiPageWikiLink Pythagorean_theorem.
- Mathematical_fallacy wikiPageWikiLink Q.E.D..
- Mathematical_fallacy wikiPageWikiLink Root_of_a_function.
- Mathematical_fallacy wikiPageWikiLink Solution_of_triangles.
- Mathematical_fallacy wikiPageWikiLink Square_root.
- Mathematical_fallacy wikiPageWikiLink Triangle.
- Mathematical_fallacy wikiPageWikiLink Truth.
- Mathematical_fallacy wikiPageWikiLink Validity.
- Mathematical_fallacy wikiPageWikiLink Zero_of_a_function.
- Mathematical_fallacy wikiPageWikiLink File:Fallacy_of_the_isosceles_triangle2.svg.
- Mathematical_fallacy wikiPageWikiLinkText "Howler".
- Mathematical_fallacy wikiPageWikiLinkText "Howlers".
- Mathematical_fallacy wikiPageWikiLinkText "Mathematical fallacy".
- Mathematical_fallacy wikiPageWikiLinkText "Mathematical fallacy#All numbers equal all other numbers".
- Mathematical_fallacy wikiPageWikiLinkText "Mathematical fallacy#Division by zero".
- Mathematical_fallacy wikiPageWikiLinkText "Mathematical fallacy#Howlers".
- Mathematical_fallacy wikiPageWikiLinkText "fallacies of mathematics".
- Mathematical_fallacy wikiPageWikiLinkText "fallacy".
- Mathematical_fallacy wikiPageWikiLinkText "howlers".
- Mathematical_fallacy wikiPageWikiLinkText "logical fallacy".
- Mathematical_fallacy wikiPageWikiLinkText "mathematical fallacies".
- Mathematical_fallacy hasPhotoCollection Mathematical_fallacy.
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- Mathematical_fallacy wikiPageUsesTemplate Template:Harv.
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- 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 Argument.
- Mathematical_fallacy type Fallacy.
- Mathematical_fallacy type Proof.
- Mathematical_fallacy type Technique.
- Mathematical_fallacy type Theorem.