Definition 4

Let $\mathfrak{F}$ be a set of sets and let $\Phi$ be the family of sets defined by the identity mapping of $\mathfrak{F}$. The union of the sets of $\Phi$ and (if $\mathfrak{F}$ is not empty) the intersection of the sets of $\Phi$ are called, respectively, the union and the intersection of the sets of $\mathfrak{F}$, and are denoted by $\bigcup_{X \in \mathfrak{F}} X$ and $\bigcap_{X \in \mathfrak{F}} X$.

If follows immediately from Proposition 1 that if $(X_\iota)_{\iota \in I}$ is a family of sets, then the union and (if $I \neq \emptyset$) the intersection of the family are respectively equal to the union and the intersection of the sets of the set of elements of this family.