Shorthand for elements in a set and elements in a vector/list? Really basic notation questions ahead. For both cases below, suppose I have an arbitrary set of integers $S$, e.g., $S = \\{2, 4, 6, 8\\}$. 1. I want to define a list/vector whose elements are subscripted by the elements in $S$, so that $x = \langle x_2, x_4, x_6, x_8 \rangle$. Is $x = \langle x_i \rangle_{i \in S}$ standard notation? 2. Exact same question, but for a set: I want to define a set whose elements are subscripted by the elements in $S$, so that $Y = \\{ y_2, y_4, y_6, y_8\\}$. Is $Y = \\{ y_i \\}_{i \in S}$ standard notation? 3. Does the answer change if $S$ contains all integers from 1 to $s$, i.e., $S = \\{1, ..., s\\}$?

I disagree with Oscar about part 1 of the question. The elements of a list or vector are ordered, but the elements of a set are not. I don’t think many (any?) mathematicians would write $x = \langle x_i \rangle_{i \in S}$ when $S=\\{4,2,8,6\\}$. Since $x_i$ is a common notation for the $i$-th element of a sequence or vector, one might be okay if $S=\\{1,\dots s\\}$, but I would more likely write $x = \langle x_i \rangle_{i=1\dots s}$ (or $\langle x_i \rangle_{i=2,4,6,8}$ ) to make the order clear if there were a reason to use subscript notation.