0
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ Why do you put equality between $S_{ABC}$ and your ideas of the sum notation? I thought that $S_{ABC}$ is the tuple and not its sum. $\endgroup$ – user87690 Nov 4 '14 at 10:25
  • $\begingroup$ Note the commas. $S_{A,B,C}$ could mean that its a tuple and $S_{ABC}$ is the sum of it. So $S_{A,B,C} != S_{ABC}$. $\endgroup$ – Thomas Fankhauser Nov 4 '14 at 10:37
  • $\begingroup$ Ok, but at least I missed the the difference when reading, so maybe it's prone to misread. $\endgroup$ – user87690 Nov 4 '14 at 10:46
  • $\begingroup$ Thanks, you're right. It is pretty much misleading. I'll update it. $\endgroup$ – Thomas Fankhauser Nov 4 '14 at 11:11
3
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ Okay thanks, that's much easier, yes. $\endgroup$ – Thomas Fankhauser Nov 4 '14 at 11:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.