I have a question about the proper notation of the following (simplified) example:
I want to express that I have a value alpha, which is the maximum of a set of n values. Each value in the set is the result of a function $f(x)$, and the range of $x$ is between $1$ and $n$.
So something like
$$\alpha = \max(\{f(x) : x = 1,\ldots,n\}).$$
Is this a proper notation? If not, how would I properly express this? It's too long ago for me studying this sort of thing to convince myself I'm writing it down right.
Best Answer
Your notation looks fine. You could also use the more informal $\alpha = \max(\{f(x_1),\ldots,f(x_n)\})$ or even $\alpha = \max(f(x_1),\ldots,f(x_n))$.
Finally, you could say that $\alpha$ is the maximum (or maximal) value among $f(x_1),\ldots,f(x_n)$, or that $\alpha$ is the maximum (or maximal) value attained by $f$ on the points $x_1,\ldots,x_n$.