Assume we have several variables of the form $d_c$ which namely can be $d_1$, $d_2$, ..., $d_n$. I want to use mathematical notation to show for which index $c$ the value of $d_c$ is minimal for all variables.
I can write the minimum value of these variables like this: $$ d_{min} = \min\left\{d_1, d_2, \ldots, d_n\right\}$$
What I need now is to find $c$ so that $d_{min}=d_c$.
The context is the following: I have several classes $1\leq c \leq n$ that have a certain value assigned to their corresponding variables $d_c$. I'm interested to know for which class this value is minimal. Let's do a small example: $$d_1 = 20\qquad d_2=15\qquad d_3=8\qquad d_4=12\qquad d_5=42$$ $$ d_{min} = \min\left\{d_1, d_2, d_3, d_4, d_5\right\} = 8$$ $$d_{min}\overset{!}{=}d_c \quad \Longrightarrow \quad c=3$$
So class number $3$ has the smallest value assigned to its corresponding variable.
- What mathematical notation can I use to find $c$?
I'm open for a totally different notation as well. Maybe this can be rewritten completely to make it much simpler and clearer to understand.