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Pathological (mathematics)

Mathematical phenomena whose properties are counterintuitive / From Wikipedia, the free encyclopedia

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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.[1]

The Weierstrass function is continuous everywhere but differentiable nowhere.