8

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?

Michael Hardy
  • 1
gnychis
  • 267
  • 1
  • 3
  • 9
  • 2
    I just use $\max$. Are you sure the maximum exists, though? Perhaps you should use $\sup$ instead (http://en.wikipedia.org/wiki/Supremum). – Qiaochu Yuan Feb 28 '12 at 02:44

3 Answers3

15

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

13

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

Nate Eldredge
  • 97,710
  • For me this would mean the supremum. – Qiaochu Yuan Feb 28 '12 at 03:36
  • I only saw this in a boolean lattice context. –  Feb 28 '12 at 03:40
  • @QiaochuYuan: That's possible. I may have only seen it used for the maximum over a finite set. – Nate Eldredge Feb 28 '12 at 04:03
  • @NateEldredge Why on earth does max point downwards?? – dawid Jun 24 '20 at 21:45
  • 2
    @viyps: Fair question. AFAIK they're meant to be analogous with $\cup$ and $\cap$ for union and intersection, and likewise $\vee$ and $\wedge$ for logical OR and AND. Note, for instance, that the maximum of two Boolean values is the same as their logical OR; and that given two sets, one of which is contained in the other, the cardinality of their union is the maximum of their cardinalities. – Nate Eldredge Jun 24 '20 at 21:47
2

\max which looks like "$\max$" http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Commands

nance2uiuc
  • 21
  • 2