Say we have two sets like this:
$A = \{a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,a_9,a_{10}\}$ and $B = \{b_1,b_2,b_3,b_4,b_5,b_6,b_7,b_8,b_9,b_{10}\}$
I want to be able to build something like this: $[(a_{1},b_{1}),(a_{3},b_{3}),(a_{6},b_{6})),(a_{7},b_{7})]$.
So I came up with this notation:
Let A be a m-sized set like this $\{a_{1},a_{2},\cdots,a_{m}\}$.
Then I build an array of pairs like this $[(a_{j},b_{j}),\cdots,(a_{k},b_{k})]$ where $a_{i}\in A'\subseteq A$ and $b_{i}\in B'\subseteq B$, with $1 \leq j \leq i \leq k \leq m $.
The problem with the notation above is that it might appear that I must pick every $a_{i} \in A$ with $i$ between $j$ and $k$. In fact, I want the notation to capture the idea that I can build the array of pairs by picking any element $a_{i} \in A$ with $i$ between $j$ and $k$ and being able to skip some elements of $A$.
I would suggest the following notation: $[(a_{n_{1}},b_{n_{1}}),...,(a_{n_{k}},b_{n_{k}})]$ with $1\leq n_{1}\leq...\leq n_{k}\leq m$.