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Discontinuity

Illustration

Illustration

Basic definition

A discontinuity is a point at which a function jumps suddenly in value, blows up, or is undefined. The opposite of continuity.

Detailed definition

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure illustrates a discontinuity of a two-variable function plotted as a surface in R^3. In the latter case, the discontinuity is a branch cut along the negative real axis of the natural logarithm ln z for complex z. Some authors refer to a discontinuity of a function as a jump, though this is rarely utilized in the literature.

Related terms

branch cut | continuous | discontinuous | essential singularity | infinite discontinuity | isolated singularity | jump discontinuity | polar coordinates | pole | removable discontinuity | removable singularity | singularity | singular point

Educational grade level

college level (AP calculus AB)

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