pathologicalˌpæθ əˈlɒdʒ ɪ kəl
pathological
English Definitions:
pathological, pathologic (adj)
of or relating to the practice of pathology
"pathological laboratory"
pathological (adj)
caused by or evidencing a mentally disturbed condition
"a pathological liar"; "a pathological urge to succeed"
diseased, morbid, pathologic, pathological (adj)
caused by or altered by or manifesting disease or pathology
"diseased tonsils"; "a morbid growth"; "pathologic tissue"; "pathological bodily processes"
pathological (Adjective)
Pertaining to pathology.
pathological (Adjective)
Relating to or caused by a physical or mental disorder.
pathological (Adjective)
Having properties which are counterintuitive or difficult to handle.
pathological (Adjective)
Having properties that cause unusually bad behaviour, especially regarding correctness or performance.
Pathological
In mathematics, a pathological phenomenon is one whose properties are considered atypically bad or counterintuitive; the opposite is well-behaved. Often, when the usefulness of a theorem is challenged by counterexamples, defenders of the theorem argue that the exceptions are pathological. A famous case is the Alexander horned sphere, a counterexample showing that topologically embedding the sphere S² in R³ may fail to "separate the space cleanly", unless an extra condition of tameness is used to suppress possible wild behaviour. See Jordan-Schönflies theorem. One can therefore say that those searching for the "pathological" are like experimentalists, interested in knocking down potential theorems, in contrast to finding general statements widely applicable. Each activity has its role within mathematics.
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