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I am struggling notating a max in a set (or rather notation in general). I have simplified the equations to relay my question.

Let's say I have a variable $E_c$, which is defined as:

$$E_c= R_c +1$$

For $n$ items, there can be an individual $E_c$ calculated for each. I want to notate the maximum value of $E_c$ for $n$ items. Would that be:

$$\max_{n\in N}E_c$$

EAA
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    This may be helpful https://math.stackexchange.com/questions/40861/mathematical-notation-for-the-maximum-of-a-set-of-function-values – Irving Rabin Oct 09 '21 at 00:56

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$ \max_{k \in [1,2,\ldots,n]} E_c(k) $

or

$ \max_{1 \leq k \leq n} E_c(k)$

Indicating that $E_c$ is a function of $k$ is important.

Godfather
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    This is the correct notation. I would just replace $N$ with $n$ (after replacing $n$ with something else) because the OP said there were $n$ items, not $N$ items. – David K Oct 09 '21 at 01:17
  • Thanks for the replies. If I swapped the $n$ with $N$, then would it make sense for $n$ items? $$\max_{N \in[1,...,n]}E_c(N)$$ – EAA Oct 09 '21 at 01:33
  • @EAA You could do that. It might confuse some people who are more used to seeing $n\in[1,2,\ldots,N.$ I usually use a different lower-case letter for the other variable if I want $n$ to be the number of items. – David K Oct 09 '21 at 01:57
  • I replaced n with k and N with n @DavidK. – Godfather Oct 10 '21 at 04:47