We read $$\sup_{x\in X}(\sup_{y\in Y} f(x,y))$$ left to right (there's really no other choice), but Question 1: doesn't this contradict the following conventions? Stuff inside parentheses is evaluated first Composed functions (such as $\sup:X\to\mathbb{R}$ and $\sup:Y\to\mathbb{R}$) are read ri...