TITLE: Mathematical notation for the maximum of a set of function values
QUESTION [27 upvotes]: 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.

REPLY [2 votes]: The most concise notation for this is just
$$\max f[n]$$
where $f[A]$ is the image of $A$ under $f$ and $n = \{m \mid m < n\}$ is the ordinal definition of numbers (assuming you start at 0 rather than 1).