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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 ( – Qiaochu Yuan Feb 28 '12 at 2:44
up vote 8 down vote accepted

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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Personally I've never heard of argmax before. – Greg Martin Feb 28 '12 at 7:29
I have seen it a lot in (computer science) optimization classes. The context of optimization & searching makes sense I guess. – user2468 Feb 28 '12 at 13:31

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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For me this would mean the supremum. – Qiaochu Yuan Feb 28 '12 at 3:36
I only saw this in a boolean lattice context. – user2468 Feb 28 '12 at 3:40
@QiaochuYuan: That's possible. I may have only seen it used for the maximum over a finite set. – Nate Eldredge Feb 28 '12 at 4:03

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