TITLE: What's a correct symbolism for "value that maximizes"
QUESTION [6 upvotes]: Possible Duplicate:
Math notation for location of the maximum 

Given a function $f(x)$, we can normally find $\max_i f(i)$. This expression evaluates to the maximum value of $f(x)$. Sometimes, however, what is interesting isn't as much the maximum value itself, but the value at which the function reaches its maximum, whatever that might be:
$$i:f(i)=\max_t f(t)$$
In plain English, I want to know who has eaten the most $f$ruit, rather than how much he's eaten.
This is kind of cumbersome, and perhaps needlessly requires a new symbol t. Besides, this isn't entirely correct, as $f(x)$ could very well have more than one maximum:
$$I=\{i:f(i)=\max_tf(t)\}$$
Is there a nicer way to express this concept?

REPLY [9 votes]: Often one writes $\displaystyle \operatorname*{argmax}_x f(x)$ for the value of $x$ that maximizes $f(x)$.
(Despite the fact that I have frequently seen that notation for many years, I find that it's not a standard TeX operator name; one cannot type \argmax and have it understood by TeX.)