Notation for time interval

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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?

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1 Answer

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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.

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