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

Also see

 * Isolated Singularity
 * Nonremovable Discontinuity