Precedence of elements in a sequence

Question

Can I use $\prec$ to say an element $i$ precedes another element $j$ in a sequence $A$? Like $i \prec j \in A$?

For example, suppose that $T=(5,3,6,4,7,8)$ is a random permutation of $A = \{3, 4, 5, 6, 7, 8\}$. Is it correct to say $3 \prec 6$, or $5 \prec 7$?

Answer 1

{5,3,6,4,7,8} is a set. Sets are not ordered.
(5,3,6,4,7,8) is finite sequence.
It is ordered in the order of appearance:
5 first, 3 second, 6 third, etc.
The notation < could be used to indicate that order 5 < 3 < 6 ...
There is no indexing in that sequence but if clumsiness is required one could write $\{5_1, 3_2, 6_3, 4_4, 7_5, 8_6\}.$

Answer 2

Those relations $3 \prec 6, 5\prec 7$ may or may not be true depending on how your partial ordering $\prec$ is defined. The order in which the elements appear in the set is inconsequential. For example, if $\prec$ is the usual ordering $>$ on the real numbers, then the relations you have stated are false, but $6 \prec 3$ is true.

Edit after question was edited: Sure, you can do that after defining $\prec$ suitably because, to the best of my (limited) knowledge, that is not a common convention. For example, you might define it in the following way: for $a_i,a_j \in (a_1,\dots,a_n)$, $a_i \prec a_j$ if $i < j$.