Set Union

Definition

We say the set $A\cup B:=\{x:x\in A\text{ or }x\in B\}$ is the union of $A$ and $B$

Let $n\in \mathbb{N}$. $\{A_1,A_2,\dots ,A_n,\dots \}$ : Infinite collection of sets. Their union is the set of elements that belong to at least one of the sets $A_n$ :

$$\bigcup _{n=1}^{\infty }{A}_n:=\{x:x\subset A_n\}$$