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I have the following, which uses set-builder notation, and where double square brackets means take the fractional part:

$$a_k = \min\left\{ a_n\:\bigg|\:a_n =\left[\!\!\left[ \frac{nf_2}{f_1} \right]\!\!\right] \right\}_{n=1}^s$$

This reads:

$a_k$ equals the minimum value in the set, ordered by index, that contains all values of $a_n$, such that $a_n$ equals the fractional part of $nf_2$ over $f_1$, where $n$ can be considered the index of the each element, with the indexes ranging from $1$ to $s$.

For my purposes, I only require the value $k$, which is the index of the minimum value of the set in braces. I am unsatisfied with the notation I have currently, it detracts from readability. Despite searching, I cannot find any resources that do it better. There is a lot of disagreement when it comes to best set notation practice. I have found a million ways I could express this.

My questions are:

Is this notation clear enough? How would you write it? Would I be better off breaking down and simplifying my notation, supporting it with more descriptive text than I already will have to.

Thank you!

Andrés E. Caicedo
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Ewan Donovan
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  • I don't know how to make those llbracket and rrbrackets on stackexchange, but is there anything wrong with $a_k=\min\left{[n f_2/f_1]:1\le n \le s\right}$? Or maybe $a_k=\min{a_n=[nf_2/f_1]:1\le n\le s\text{ and }n\in\mathbb{N}}$ if you want to be a little more precise about $n$ and $a_n$. In words I suppose you could also say that $1\le k\le s$ is such that $[k f_2/f_1]$ is least. – JunderscoreH Jul 13 '19 at 22:32
  • About the brackets, I use [![ ]!], the ! is like a 'negative space' kind of thing, just as : adds space. Your response is satisfactory! There's nothing wrong with what you suggested, I appreciate your reply! I would upvote you if I had the reputation on this platform. – Ewan Donovan Jul 13 '19 at 23:48

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