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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?

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    @ThomasAndrews I am very well aware. Did I make that confusion anywhere in the page?2011-12-23

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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.)

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    @TomHale : $\uparrow$ (Just in case you missed this.)2017-08-10