Definition:Removable Discontinuity

Real Functions of One Variable
Let $f$ be a real function which is continuous on some open interval $\left({a \,.\,.\, b}\right)$ except at some point $c$ where it has a discontinuity.

If $f$ can be made continuous at $c$ by defining (or redefining) $f \left({c}\right)$ then the discontinuity at $c$ is said to be removable.

Also see

 * Definition:Isolated Singularity
 * Definition:Nonremovable Discontinuity


 * Definition:Jump Discontinuity
 * Definition:Discontinuity of the First Kind