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.