How to sum a multiset

Question

I'd like to express the sum of every element in a multiset using sigma and/or universal quantification.

Let A be a multiset. The function of x equals the sum of every element of A. x should equal 8.

$$A = \{1, 2, 2, 3\}$$

Thank you,

Answer 1

You should use some kind notation for every element of the multiset A, like $a_{i}$.

Like for this example here if $ A = \lbrace 1, 2, 2, 3 \rbrace $, then $a_{1} = 1$, $a_{2} = 2$, $a_{3} = 2$ and $a_{4} = 3$.

Now you can sum over all the elements of the multiset by $$\sum_{i=1}^4 a_{i} = a_{1} + a_{2} + a_{3} + a_{4} = 1 + 2 + 2 + 3 = 8$$