Analogously, the right-hand one-sided limit at is the real number such that for every there exists a such that whenever .
Common notations for the one-sided limits are
Sometimes, left-handed limits are referred to as limits from below while right-handed limits are from above.
Theorem The ordinary limit of a function exists at a point if and only if both one-sided limits exist at this point and are equal (to the ordinary limit).
Example The Heaviside unit step function, sometimes colloquially referred to as the diving board function, defined by
|Date of creation||2013-03-22 12:40:28|
|Last modified on||2013-03-22 12:40:28|
|Last modified by||CWoo (3771)|
|Synonym||limit from below|
|Synonym||limit from above|
|Defines||Heaviside unit step function|