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I have a set of variables that have a value, and i want to find the max of those values.

Here is the equivalent of what I want to do with "sum"

$\sum_{j:~N_j \in U_i}~ DA_j$

For all j subject to $N_j \in U_i$, then sum $DA_j$. Except I want a max. What is the right symbol to use?

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    I just use $\max$. Are you sure the maximum exists, though? Perhaps you should use $\sup$ instead (http://en.wikipedia.org/wiki/Supremum).2012-02-28

3 Answers 3

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If you are interested of the maximum value of $DA_j$ under the condition that $N_j \in U_i$ then you can use $\max$ as in: $\max_{j : N_j \in U_i} DA_j$ But if you are interested in the value of $j$ that makes $DA_j$ maximal, then you can use $\operatorname{argmax}$ as in: $\operatorname{argmax}_{j : N_j \in U_i} DA_j$

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    I have seen it a lot in (computer science) optimization classes. The context of optimization & searching makes sense I guess.2012-02-28
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Some people write $\bigvee_{j : N_j \in U_i} D A_j$ with $\bigwedge$ for min. I'm not convinced it's clearer than $\max$. (The infix usage is more common, and more elegant looking: $a \vee b$ versus $\max\{a,b\}$.)

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    @QiaochuYuan: That's possible. I may have only seen it used for the maximum over a finite set.2012-02-28
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\max which looks like "$\max$" http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Commands