What are the values of the sum?

Question

what are the values of $\sum_{j \in S} 1$, where S = {1, 3, 5, 7}.

if we have $\sum_{j = 1}^{n} 1$ then the answer will be n. But what happens if this a set?

Answer 1

For any set $S$, we have $$\sum_{j \in S} 1 = 1 + 1 + \cdots + 1 = \#S$$ where #S denotes the number of elements of $S$.