removable discontinuity

A single-point hole in a graph that could be patched by defining (or redefining) one value.

A removable discontinuity occurs at $x=a$ when $\lim_{x\to a} f(x)$ exists but either $f(a)$ is undefined or $f(a)$ disagrees with that limit — the graph has a hole that redefining $f(a)$ would fill.

Examples

$f(x)=\dfrac{x^2-1}{x-1}$ has a removable discontinuity at $x=1$ , since the factor $(x-1)$ cancels and the limit there is $2$ .