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!