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When I write $\text{min}_x f(x)$ I always read it as "the minimum value of $f(x)$" over some given range.

I am wondering, what is the standard notation for writing "the parameter that achieves a minimum (or maximum)"

Eg. I have a function $f(x)$ and I want to write, using notation, the value $x$ that gives the smallest value for $f(x)$.

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The common notation for this is

$\arg \min_{x} f(x)$

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