In mathematics, a one-sided limit is where the limit of a function is defined in moving in the positive or negative direction, but not both.

For example, consider the function

Now, if we take the limit moving from smaller values of x to 1, noted,

but if we take the limit moving from larger values of x to 1, noted,

These two limits are not identical and so f has a one-sided limit at the point x=1.

If these two limits are identical, f is said to have a two-sided limit at that point.

See also: Two-sided limit