TITLE: Notation for choosing the k smallest elements from a set of integer
QUESTION [7 upvotes]: Is there any specific notation for picking $k$ elements from a set which are the smallest?
Ex:
{$1,3,5,7,9,11$} with $k = 3 \Rightarrow$ We want $1,3,5$

REPLY [2 votes]: I haven't seen a notation for this. One idea would be to conceptualize it in terms of sequences, like so:
Definition. Let $X$ denote the set of interest. Then we will write $X^\sim$ for the unique sequence defined as follows.

$X_0^\sim$ is the empty set
$X_{i+1}^\sim = X_i^\sim\cup \{\mathrm{min}(X \setminus X_i^\sim)\}$

For example, $\{1,3,5,7,9,11\}_3^\sim = \{1,3,5\}.$
If its going to be used repeatedly, just tell the reader that you will tend to omit the superscript when no ambiguity arises. E.g $\{4,5\}_1 = \{4\}$.