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Math Help - Valid sum over binary variables, basic question

  1. #1
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    Valid sum over binary variables, basic question

    given the binary variables: y_i, x_i, i = 1,..,5
    where
    <br />
\sum_{i=1}^5 x_i = \sum_{i=1}^5 y_i = 1<br />

    Show that
    <br />
\sum_{i=1}^t x_i \leq \sum_{i = 1}^{t} y_i, t \in \{1,\dots,5\}<br />
    implies that:
    <br />
\sum_{i=t}^5 x_i \geq \sum_{i = t}^{5} y_i, t \in \{1,\dots,5\}<br />

    Can anybody help me, to show that it holds for every index?
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  2. #2
    A Plied Mathematician
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    What is a "binary variable" in this case? What is the domain of such a variable? What kind of addition are you doing here?
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