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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.

3 Answers 3

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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 $x_1,\ldots,x_n$.

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    I prefer $\max\{f(x_1,\ldots,f(x_n)\}$ with curly braces and no parentheses. In this instance, the parentheses don't actually help, and the curly braces remind you that the thing whose maximum is sought is a set rather than a tuple.2018-08-08
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According to Wikipedia you don't need the commas.

$\alpha = \max \{ f(x) : x = 1 .. n \}$

Alternatively:

$\alpha = \max \{ f(x) : x \in \mathbb{Z} \land 1\geq x \geq n \}$

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    Never seen that notation before in my life. I would probably infer its meaning from the context, but I'd feel befuddled. Almost as befuddled as why this question from 7 years ago needed a new answer, to be honest.2018-08-08