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- Classification_of_discontinuities abstract "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.Consider a real valued function ƒ of a real variable x, defined in a neighborhood of the point x0 at which ƒ is discontinuous. Three situations can be distinguished:The term removable discontinuity is sometimes used by abuse of terminology for cases in which the limits in both directions exist and are equal, while the function is undefined at the point . This use is abusive because continuity and discontinuity of a function are concepts defined only for points in the function's domain. Such a point not in the domain is properly named a removable singularity.The oscillation of a function at a point quantifies these discontinuities as follows: in a removable discontinuity, the distance that the value of the function is off by is the oscillation; in a jump discontinuity, the size of the jump is the oscillation (assuming that the value at the point lies between these limits from the two sides); in an essential discontinuity, oscillation measures the failure of a limit to exist.↑".
- Classification_of_discontinuities thumbnail Discontinuity_removable.eps.png?width=300.
- Classification_of_discontinuities wikiPageExternalLink Discontinuity.
- Classification_of_discontinuities wikiPageID "2661487".
- Classification_of_discontinuities wikiPageRevisionID "592853488".
- Classification_of_discontinuities first "L.D.".
- Classification_of_discontinuities hasPhotoCollection Classification_of_discontinuities.
- Classification_of_discontinuities id "4447".
- Classification_of_discontinuities id "Discontinuity_point".
- Classification_of_discontinuities last "Kudryavtsev".
- Classification_of_discontinuities oldid "12112".
- Classification_of_discontinuities title "Discontinuity point".
- Classification_of_discontinuities title "Discontinuity".
- Classification_of_discontinuities title "Discontinuous".
- Classification_of_discontinuities urlname "Discontinuity".
- Classification_of_discontinuities subject Category:Mathematical_analysis.
- Classification_of_discontinuities comment "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.".
- Classification_of_discontinuities label "Clasificación de discontinuidades".
- Classification_of_discontinuities label "Classification of discontinuities".
- Classification_of_discontinuities label "Discontinuïteit".
- Classification_of_discontinuities label "Punkt nieciągłości".
- Classification_of_discontinuities label "Punto di discontinuità".
- Classification_of_discontinuities label "Unstetigkeitsstelle".
- Classification_of_discontinuities label "不连续点".
- Classification_of_discontinuities label "不連続性の分類".
- Classification_of_discontinuities sameAs Unstetigkeitsstelle.
- Classification_of_discontinuities sameAs Clasificación_de_discontinuidades.
- Classification_of_discontinuities sameAs Punto_di_discontinuità.
- Classification_of_discontinuities sameAs 不連続性の分類.
- Classification_of_discontinuities sameAs 불연속성의_분류.
- Classification_of_discontinuities sameAs Discontinuïteit.
- Classification_of_discontinuities sameAs Punkt_nieciągłości.
- Classification_of_discontinuities sameAs m.07w4f1.
- Classification_of_discontinuities sameAs Q541961.
- Classification_of_discontinuities sameAs Q541961.
- Classification_of_discontinuities wasDerivedFrom Classification_of_discontinuities?oldid=592853488.
- Classification_of_discontinuities depiction Discontinuity_removable.eps.png.
- Classification_of_discontinuities isPrimaryTopicOf Classification_of_discontinuities.