StellarA removable discontinuity occurs when the limit of a function exists at a point, but the function is either undefined there or has the wrong value. Since the nearby behavior is already heading toward a single number, the discontinuity can be “removed” by redefining the function value at that point to match the limit. This makes the function continuous there without changing how it behaves elsewhere.
This idea is important because it shows that not every discontinuity is equally serious. Some discontinuities come from a small mismatch at one point rather than a deeper problem in the function’s behavior. If the limit exists, then the graph is almost continuous already, often with just a hole. By filling that hole at the correct y-value, we can turn the function into a continuous one at that point.