One-sided limit
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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
- <math>f(x) =
\left\{
\begin{matrix}
1\ \mbox{if}\ x\isin (-\infty, 1] \\
0\ \mbox{if}\ x\isin (1, \infty) \\
\end{matrix}\right.<math>
Now, if we take the limit moving from smaller values of x to 1, noted,
- <math>\lim_{x\rarr 1} f(x) = 1<math>
but if we take the limit moving from larger values of x to 1, noted,
- <math>\lim_{x\rarr 1^{-}} f(x) = 0<math>
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