You can define like that the maximum of any finitely many elements.
When the parameters are an infinite set of values, then it is implied that one of them is maximal (namely that there is a greatest one, unlike the set $\{-\frac{1}{n} | n\in\mathbb{N}\}$ where there is no greatest element)
The meaning will depend on context. Here it means that for each triple $\langle x,y,z\rangle$ such that $xyz=1$ we find the maximum of $x+y,x+z$, and $y+z$, and then we find the smallest of those maxima: it’s
$$\min\Big\{\max\{x+y,x+z,y+z\}:xyz=1\Big\}\;.$$
In general it will be something similar: you’ll be finding the minimum of some set of maxima.
Best Answer
Taking the maximal number amongst the parameters.
$\max\{x_1,x_2\} = \cases{x_1, \text{if }x_1 > x_2\\x_2, \text{otherwise}}$
You can define like that the maximum of any finitely many elements.
When the parameters are an infinite set of values, then it is implied that one of them is maximal (namely that there is a greatest one, unlike the set $\{-\frac{1}{n} | n\in\mathbb{N}\}$ where there is no greatest element)