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Pathological (mathematics)

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 or nice. These terms are sometimes useful in mathematical research and teaching, but there is no strict mathematical…

In algebraic geometry, Well-behaved & Pathological examples

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In analysis

In topology

In algebraic geometry

Well-behaved

Pathological examples

Computer science

Exceptions

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Pathological (mathematics)

Nodes177
Edges176
Triples2
Avg. degree1.99
Density0.011299
Components1

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pathological function better-behaved functions continuous general well-behaved example differentiable examples mathematical smooth set sets pathologies theory topology everywhere real algebraic

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SubjectPredicateObjectConfidenceSrc
the Black-Scholes model in finance.Counterexamples in Analysis is a whole book of such counterexamples.Another example of pathological function is Du-Bois Reymond continuous functioninstance ofnowhere differentiable functions have been shown to appear in basic physical and biological processes such as Brownian motion and in applications0.80text
that can't be represented as a Fourier seriesinstance ofnowhere differentiable functions have been shown to appear in basic physical and biological processes such as Brownian motion and in applications0.80text

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