Notation of the summation of a set of numbers Given a set of numbers $S=\{x_1,\dotsc,x_{|S|}\}$, where $|S|$ is the size of the set, what would be the appropriate notation for the sum of this set of numbers? Is it 

$$\sum_{x_i \in S} x_i
\qquad\text{or}\qquad
\sum_{i=1}^{|S|} x_i$$ or something else?
I'd write either $\displaystyle\quad\sum_{i=1}^{|S|} x_i\quad$ or $\displaystyle\quad\sum_{x\in S} x$.

If the second form is used, then the subscript is just clutter.

Some mathematicians (perhaps especially set theorists?) might write $\displaystyle \sum S$.  This would parallel the way set theorists write $\displaystyle \bigcup S$ where others might write $\displaystyle \bigcup_{x\in S} x$.
Say I had a set A, under an operation with the properties of $+$, then $$\sum_{i\in A} x_i$$ is how I write it.