Jump Discontinuity/Examples/Example 2

Example of Jump Discontinuity
Let $f: \R \to \R$ be the real function defined as:
 * $\forall x \in \R: \map f x = \begin {cases} 0 & : x > 1 \\ 1 & : x < 1 \\ \dfrac 1 2 & : x = 1 \end {cases}$

Then $f$ has a jump discontinuity at $x = 1$.

In this case, $\map f 1$ is defined, but equals neither limit.