Get Math Help

GET TUTORING NEAR ME!

(800) 434-2582

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    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. Though defined identically, discontinuities of univariate functions are considerably different than those of multivariate functions. One of the main differences between these cases exists with regards to classifying the discontinuities, a caveat discussed more at length below.

    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)

    Back to List | POWERED BY THE WOLFRAM LANGUAGE