\bigcupThe \bigcup operator represents the union of a collection of sets. It is often used in mathematical contexts to denote the union of multiple sets, typically indexed by some parameter. The union of sets is a fundamental operation in set theory, combining all elements from the involved sets into a single set without duplication.
Union of a sequence of sets A_i from i=1 to n
\bigcup_{i=1}^{n} A_iUnion of singleton sets generated by a function f over a domain X
\bigcup_{x \in X} \{ f(x) \}Union of a collection of sets S_k indexed by natural numbers
\bigcup_{k \in \mathbb{N}} S_k