About: Pathological (mathematics)

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In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. On the other hand, if a phenomenon does not run counter to intuition, it is sometimes called well-behaved. These terms are sometimes useful in mathematical research and teaching, but there is no strict mathematical definition of pathological or well-behaved.

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rdf:type	Thing
rdfs:label	Pathologisches Beispiel (de) Cas pathologique (fr) 病的な (数学) (ja) Pathological (mathematics) (en) Patologia (matemática) (pt) 病态 (数学) (zh)
rdfs:comment	In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. On the other hand, if a phenomenon does not run counter to intuition, it is sometimes called well-behaved. These terms are sometimes useful in mathematical research and teaching, but there is no strict mathematical definition of pathological or well-behaved. (en) 数学における病的な（びょうてきな、英語: pathological; 病理学的な）事象とは、その性質が変則的に悪質であったり、直感に反すると見なされるようなもののことを言う。素性の悪い（ill-behaved）ともいう。対義語には (well-behaved) というものがある。 (ja) Em matemática, uma patologia ou exemplo patológico é um exemplo daquilo que não é intuitivamente esperado. Patologias têm sido utilizadas na matemática para diversos fins: * Justificar o formalismo e o rigor. * Expor as limitações de certas teorias e justificar teorias mais gerais. A função de Dirichlet, por exemplo, não é integrável no sentido de Riemann mas o é no sentido de Lebesgue. * Fornecer contra-exemplo a conjecturas. (pt) 在数学中，病态（英語：Pathological）现象是指其性质被认为是非典型的或反直觉的现象，反义词为良态（Well-behaved）。 (zh) Pathologische Beispiele sind besondere Beispiele, welche oftmals in mathematischen Kontexten auftreten. Definitionen mathematischer Objekte sind teilweise durch Anschauung motiviert, wie zum Beispiel die Definition des Wegzusammenhangs. Bei einem pathologischen Beispiel wird ein Objekt konstruiert, das den Bedingungen einer mathematisch exakten Definition entspricht, jedoch in Konflikt zu der zugrundeliegenden Anschauung steht oder für weitere Beweise unerwünschte Eigenschaften aufweist, die als untypisch für üblicherweise auftretende Fälle angesehen werden. In der Regel sind pathologische Beispiele auch Gegenbeispiele. (de) En mathématiques, un objet pathologique est un objet qui s'oppose à l'intuition que l'on a de la situation générale. Par exemple, la fonction de Weierstrass, qui est une fonction continue nulle part dérivable, peut être considérée comme pathologique car elle s'oppose à l'intuition que l'on a des fonctions continues. Ainsi, Henri Poincaré écrit à leur sujet : (fr)
differentFrom	Good behaviour (disambiguation)
foaf:depiction
dcterms:subject	Mathematical terminology
Wikipage page ID	372742 (xsd:integer)
Wikipage revision ID	1124013366 (xsd:integer)
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