# What does discontinuity mean in math?

##### 1 Answer

A function has a discontinuity if it isn't well-defined for a particular value (or values); there are 3 types of discontinuity: infinite, point, and jump.

Many common functions have one or several discontinuities. For instance, the function

Notice that there the curve does not cross at

In a similar way, the periodic function

Infinite discontinuities occur in rational functions when the denominator equals 0.

Point discontinuities occur where when you find a common factor between the numerator and denominator. For example,

has a point discontinuity at

Point discontinuities also occur when you create a piecewise function to remove a point. For example:

has a point discontinuity at

Jump discontinuities occur with piecewise or special functions. Examples are floor, ceiling, and fractional part.