TITLE: Standard Indicator function?
QUESTION [6 upvotes]: Is there any standard function that outputs $1$ if an inequality is true and $0$ otherwise? e.g 
$$F =
\begin{cases}
1 & \text{if }x>D\\
0 & \text{otherwise}
\end{cases}$$

REPLY [2 votes]: The problem with using the Heaviside function is that there are several conventions at to what $H(0)$ should equal. Sometimes it is $0$, sometimes it is $\frac{1}{2}$, sometimes it is $1$. To avoid ambiguity, we can write the Kronecker delta $f(x) = H(x) \cdot (1-\delta_{0,x})$; this ensures that $$f(x) =\left\{ \begin{aligned} &0 & x \leq 0 \\ &1 & x > 1 \end{aligned} \right.$$
In the case of the particular example that you gave, this would be $F(x) = H(x-D) \cdot (1-\delta_{D,x})$.
Given all this, I think Yuval Filmus's answer with the indicator function $\Bbb{1}_{x>D}$ is simpler.