1

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?

ScottishTapWater
  • 117
  • It's not going to really be possible to write your formula in a mathematically perfect way because the term "event" hasn't been defined. In particular, an "event" has an associated value of the time it occurred at, which is crucial to forming your formula. To write it mathematically you'll need a function that given an event outputs the time it occurred at (or something equivalent). –  Nov 27 '20 at 01:18
  • But if you're willing to be a bit informal then you can do it. –  Nov 27 '20 at 01:21
  • 1
    @SenZen is it understandable enough? I'm not too bothered about whether its formally correct if there's no simple way to do it formally given it's going in an electronics paper not a maths one. – ScottishTapWater Nov 27 '20 at 01:34

1 Answers1

0

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.