zones of discontinuity - significado y definición. Qué es zones of discontinuity
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Qué (quién) es zones of discontinuity - definición

POINT AT WHICH A FUNCTION IS NOT CONTINUOUS
Discontinuous; Removable discontinuity; Essential discontinuity; Types of discontinuity; Jump discontinuity; Discontinuity of the first kind; Discontinuity of the second kind; Discontinuity (mathematics); Jump point; Step discontinuity; Discontinuously; Infinite discontinuity; Jump discontinuities; Jump (mathematics)
  • The function in example 3, an essential discontinuity
  • The function in example 2, a jump discontinuity
  • The function in example 1, a removable discontinuity

discontinuous         
A process that is discontinuous happens in stages with intervals between them, rather than continuously.
= intermittent
ADJ
Classification of discontinuities         
Continuous functions are of utmost importance in mathematics, functions and applications. However, not all functions are continuous.
discontinuous         
a.
Interrupted, broken, intermittent, discrete.

Wikipedia

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.

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 of the two sides);
  • in an essential discontinuity, oscillation measures the failure of a limit to exist; the limit is constant.

A special case is if the function diverges to infinity or minus infinity, in which case the oscillation is not defined (in the extended real numbers, this is a removable discontinuity).