I'm trying to write the following using sensible notation:
In the time period between now and M units ago, if n > 0 output 1, if n = 0 output 0. Where n is the number of events that have occurred in the time period.
I think I can write that as:
\begin{equation}
\label{eqn:algdef}
\mbox{for }[t-M,t]\mbox{ } B = \left\{
\begin{array}{lll}
1 & for & n > 0\\
0 & for & n = 0
\end{array}
\right.
\end{equation}
However, I'm an engineer, not a mathematician and I want to check that that this notation makes sense.
If it doesn't what's the better way to do this?
Best Answer
If you want understandability and not formality here's what I'd go for:
$B(M) = \begin{cases} 1: & E_M \neq \emptyset \\ 0: & E_M = \emptyset \end{cases}$
Where $E_M$ is the set of events that happen between time $(t - M)$ and $t$:
$E_M = \{ e_p: e_p \in E \text{ and } t-m \leq p \leq t\}$
Where $e_p$ is an event that occurs at time $p$, and $E$ is the set of all events.