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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?