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.
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