# What does discontinuity mean in math?

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.

By signing up, you agree to our Terms of Service and Privacy Policy

In mathematics, discontinuity refers to a point or interval where a function is not continuous. It occurs when there is a break or jump in the graph of a function, meaning that the function fails to have a smooth and unbroken path. Discontinuities can be classified into three main types: removable, jump, and essential discontinuities. Removable discontinuities can be fixed by redefining the function at that specific point, while jump and essential discontinuities cannot be removed or fixed.

By signing up, you agree to our Terms of Service and Privacy Policy

- What is jump discontinuity in math?
- How do you prove that the limit of #(2x^2 + 1) = 3 # as x approaches 1 using the epsilon delta proof?
- How do you find the limit of #(e^x - cos x -2x)/(x^2 -2x) # as x approaches 0?
- How do you use a graphing calculator to find the limit of #xabs(x-4)# as x approaches -1?
- How do I find the limits of rational functions?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7