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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!

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  • $\begingroup$ I would say that you have an ordered pair $S=(a_1,\cdots,a_n)$ and a set $S'=\{x_l:1\le l\le k,\mbox{ where each } x_i=a_j\mbox{ for some }j\}$. $\endgroup$ Commented Sep 18, 2015 at 15:14
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    $\begingroup$ I'm a little confused. Let's say $S$ has 5 elements, so then $n = 5$. Then what is $K$? $1 \leq K \leq n$? $\endgroup$ Commented Sep 18, 2015 at 17:46

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$$S=\{a_1,...,a_n\}, n\in \mathbb N$$ $$S'=\{b_1,...b_k\}, k\in \mathbb N$$ $$S'\subseteq S$$

This is my approach, don't know for sure this is the best way. $S'\subseteq S$ means, $S'$ is a subset from $S$.

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  • $\begingroup$ I like this way. I think it is quite practical. Thanks for your help! $\endgroup$ Commented Sep 18, 2015 at 16:50
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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.

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