What is a limit from below?

Aug 14, 2018

If we have a limit from below, that is the same as a limit from the left (more negative).

We can write this like the following:
${\lim}_{x \to {0}^{-}} f \left(x\right)$
${\lim}_{x \to 0} f \left(x\right)$
This is generally more interesting with a Piecewise function. Imagine a function which is defined as $y = x$ for $x < 0$ and $y = x + 1$ for $x > 0$. We could imagine at that 0 there is a little jump. It should look like this:
The limit as $x \to 0$ from below is clearly 0 while from above is clearly 1. That means the limit does not exist and there is a jump discontinuity at $x = 0$.