It might therefore not be considered wrong to use singular forms of abbreviations with plural numbers. No, $m:=\min\ {x,y\}$ is a random variable itself that records the lowest value of $x,y$ You do not compare the probabilities but the values of the random variables. So yes, it's a function that, taken two elements, gives you the minimum of those. The space between arg and min is confusing It would better be written argmin
What the operator argmin does, when applied to a function, is pick out the point in the function's domain at which the function takes its minimum value (assuming that the point is unique). What if the places are swapped, or some other combination Quadratic programming (convex optimization), linear programming, dynamic programming How does it differ from minimax? Find local max, min, concavity, and inflection points ask question asked 11 years ago modified 10 years, 11 months ago Define $\arg\min_x f (x)$ as the set of values of $x$ for which the minimum of $f (x)$ is attained, so it is the set of values where the function attains the minimum.
Properties of min (x,y) and max (x,y) operators ask question asked 5 years, 4 months ago modified 5 years, 4 months ago 6 minimum is reached, infimum (may) not That is, the numbers of the form $1/n$ have an inf (that is, 0), while the natural numbers have a min (that is, 1).
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