The first discontinuity is 1. Removable discontinuity: If LIMF (x) = a (when x approaches X0) but A is not equal to x0 or f(x0) is undefined. 2. Jump discontinuity: If LIMF (x) (x→ x ο-) and limf(x)(X→Xο+) exist but are not equal.

The second kind of discontinuity: If at least one of LIMF (x) (x→ Xο-) and limf(x)(X→Xο+) does not exist, then the point Xο is the second kind of discontinuity.