Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
2  
I just use $\max$. Are you sure the maximum exists, though? Perhaps you should use $\sup$ instead (en.wikipedia.org/wiki/Supremum). –  Qiaochu Yuan Feb 28 '12 at 2:44
add comment

3 Answers

up vote 6 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: $$\operatorname{argmax}_{j : N_j \in U_i} DA_j$$

share|improve this answer
1  
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
add comment

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 $\max\{a,b\}$.)

share|improve this answer
    
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
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.