In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability. See Singularity theory for general discussion of the geometric theory, which only covers some aspects.In real analysis singularities are also called discontinuities. There are three kinds: type I, which has two sub-types, and type II, which also can be divided into two subtypes, but normally is not.

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