I'm currently confused in how to express the sum of a tuple. I have a set or a tuple (for summation, order shouldn't be an issue) like this:
$$S_{A,B,C} = (1,3,6)$$
The subscript $A,B,C$ has nothing to do with the elements of the tuple, it identifies the exact type of S and is there to illustrate the variable naming.
I want to simply add all components: $1+3+6 = 10$.
My initial try was this:
$$X_{A,B,C} = \sum_{x \in S_{A,B,C}} x.$$
The next:
$$X_{A,B,C} = \sum_{x=1}^{|S_{A,B,C}|} S_{A,B,C,x}$$
But I was told that both versions are hard to read.
How would you recommend to write it?
I think that $X_{A, B, C} = ∑ S_{A, B, C} = ∑ (1, 3, 6) = 10$ works and is even formally correct. $∑_{i ∈ I} f(i)$ is a variant of $∑(f(i): i ∈ I) = ∑f$. The argument you give to a sum operator is a function rather than set, the same element can be there more times. And an $n$-tuple is a function from a set of form $\{1, …, n\}$ or $\{0, …, n - 1\}$ depending on convention.