To denote repeated [[02 Areas/Math/Union|Union]] or [[02 Areas/Math/Intersection|Intersection]] [[Operation|Operations]] on a group of [[02 Areas/Math/Set|Sets]], similar to [[Sigma Notation]] or [[Product Notation]], you can denote it with the following notation: $\huge \begin{align} A_{1} \cup A_{2} \cup \dots \cup A_{n} &= \bigcup_{i=1}^{n} A_{i} =\set{x \mid \exists i \, x \in A_{i}}\\ A_{1} \cap A_{2} \cap \dots \cap A_{n} &= \bigcap_{i=1}^{n}A_{i} = \set{x\mid\forall i \, x \in A_{i} }\\ \\ A_{1} \cup A_{2} \cup \dots &= \bigcup_{i=1}^{\infty} A_{i} =\set{x \mid \exists i \, x \in A_{i}}\\ A_{1} \cap A_{2} \cap \dots &= \bigcap_{i=1}^{\infty}A_{i} = \set{x\mid\forall i \, x \in A_{i} } \end{align}$