Notation for indexing an indexed sequence. I have a notation question. Say I have the following:
$S = \{a_{1}, \ldots, a_{n}\}$ a finite list of integers (order matters).
What I really want is to express that now I pick only $K$ elements, in any order.
So, I came up with this idea $S'  =  \{a_{i_1}, \ldots, a_{i_k}\}$ where $i$ ranges from 1 to $n$. Is it somehow correct?
Thanks in advance!

Not entirely correct. Note that the footnotes $1, \dots, k$ already indicate that you chose $k$ elements. If you want to select distinct $k$ elements out of $S$, then saying something like "Let $1 \leq i_{1} < \cdots < i_{k} \leq n$" is clear enough.
