# Valid sum over binary variables, basic question

• Sep 15th 2010, 03:48 PM
leoemil
Valid sum over binary variables, basic question
given the binary variables: y_i, x_i, i = 1,..,5
where
$
\sum_{i=1}^5 x_i = \sum_{i=1}^5 y_i = 1
$

Show that
$
\sum_{i=1}^t x_i \leq \sum_{i = 1}^{t} y_i, t \in \{1,\dots,5\}
$

implies that:
$
\sum_{i=t}^5 x_i \geq \sum_{i = t}^{5} y_i, t \in \{1,\dots,5\}
$

Can anybody help me, to show that it holds for every index?
• Sep 16th 2010, 02:25 AM
Ackbeet
What is a "binary variable" in this case? What is the domain of such a variable? What kind of addition are you doing here?