Union

For two sets, write $A\cup B=\bigcup\{A,B\}$. For an indexed family $(A_i)_{i\in I}$, the notation $\bigcup_{i\in I}A_i$ means the union of the sets in its range.

Union is dual to intersection and interacts with complement via De Morgan’s laws in an ambient universe.

• $\{1,2\}\cup\{2,3\}=\{1,2,3\}$.
• If $A_n=\{n\}$ for $n\in\mathbb{N}$, then $\bigcup_{n\in\mathbb{N}} A_n=\mathbb{N}$.