Interactive Real Analysis

Suppose f is a function with domain D and c D is a point of discontinuity of f.

1. if f(x) exists, then c is called removable discontinuity.
2. if f(x) does not exist, but both f(x) and f(x) exit, then f is called a discontinuity of the first kind, or jump discontinuity
3. if either f(x) or f(x) does not exist, then c is called a discontinuity of the second kind, or essential discontinuity.