Classification of discontinuities

The function in example 1, a removable discontinuity

The function in example 2, a jump discontinuity

The function in example 3, an essential discontinuity

Continuous functions are of utmost importance in mathematics, functions and applications. However, not all functions are continuous. If a function is not continuous at a point in its domain, one says that it has a discontinuity there. The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function. This article describes the classification of discontinuities in the simplest case of functions of a single real variable taking real values.

单词	Infinite discontinuity
释义	Infinite discontinuity 英语百科 Classification of discontinuities Continuous functions are of utmost importance in mathematics, functions and applications. However, not all functions are continuous. If a function is not continuous at a point in its domain, one says that it has a discontinuity there. The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function. This article describes the classification of discontinuities in the simplest case of functions of a single real variable taking real values.
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Infinite discontinuity

Classification of discontinuities