\begin{definition}[Definition:Dirac Delta Function/Definition 2]
Let $\epsilon \in \R_{>0}$ be a (strictly) positive real number.
Consider the real function $F_\epsilon: \R \to \R$ defined as:
:$\map {F_\epsilon} x := \begin {cases}
0 & : x < -\epsilon \\
\dfrac 1 {2 \epsilon } & : -\epsilon \le x \le \epsilon \\
0 & : x > \epsilon \end {cases}$
The '''Dirac delta function''' is defined as:
:$\map \delta x = \ds \lim_{\epsilon \mathop \to 0} \map {F_\epsilon} x$
\end{definition}