elementary set theory

I am currently trying to understand something that was stated in "Introduction to Analysis", it is the fifth edition. It is used for the Advance Calculus 1 course at ASU. I'm not taking the class right now but I want to get a jump on the material. I've taken an intro course on Logic and I've also taken a Discrete Mathematics course.

I think I understand these two definitions well. The first is "Let $\Lambda$ be a set, and suppose for each $\lambda\in\Lambda$, a subset $A_\lambda$ of a given set S is specified. The collection of sets $A_\lambda$ is called an $\textit{indexed family}$ of subsets of S with $\Lambda$ as the index set. We denote this by $\{A_\lambda\}_{\lambda\in\Lambda}$".

The second is: If $A_\lambda$ is an indexed family of sets, define $$\bigcap_{\lambda\in\Lambda} A_\lambda=\{x:x \in A_\lambda, \text{for all }\lambda \in \Lambda\}$$ and $$\bigcup_{\lambda\in\Lambda} A_\lambda=\{x:x \in A_\lambda, \text{for some } \lambda \in \Lambda\}$$ The book states that if $\Lambda$ is empty then the union will be the empty set but that it is unclear what to expect from the intersection. I don't understand why that is. If $\Lambda$ is empty then doesn't that mean that there is no index for $A_\lambda$ and that there is no way of creating the intersection and union of $A_\lambda$?