Discontinuity

For a value , let = (the limit from the left) and = (the limit from the right).

If L^- = L⁺ = , the function is continuous at .

If L^- = L⁺ ≠ , the function has a removable discontinuity at .

If L^- ≠ L⁺, and both values are finite, the function has a jump discontinuity at .

If L^- ≠ L⁺, and one or both values is infinite, the function has an infinite discontinuity at . This is also called an essential discontinuity.