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Math Help - Notation question

  1. #1
    Newbie
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    Apr 2013
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    Berlin
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    Notation question

    Hi everyone,

    I would like to state the following in a mathematical notation:

    If x is greater than 0 somewhere between time t=0 and T, then event y occurs. Here is what I have in mind:

    x_t>0 \quad \forall \quad t \in T \quad \Rightarrow \quad \text{y event}

    Is that correct? I hope you have other suggestions, because I don't think the above is "state of the art" math notation.

    Thanks a lot.
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  2. #2
    MHF Contributor
    Joined
    Sep 2012
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    Australia
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    Re: Notation question

    Hey neptunhiker.

    You might try representing y as a function of time and x as a function of time for some region of time T.

    If you define y(t) = 0 as no event occutring at time t and y(t) = 1 as an event occurring at time t, then you can say that

    y(t) = H(x(t)) where H(t) = 0 if t <= 0 and H(t) = 1 if t > 0.

    Then using this, you define y(t) as the condition of an event happening at time t which may be discrete or continuous.
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