Consider [sets](Sets.md) $A$ and $B.$ The _union_ of sets $A$ and $B$ is the set formed from the collection of all of the elements from both sets. This is denoted as $A\cup B.$ ^2ae700 # Unions of multiple sets We denote a [union](Union%20of%20sets.md) between multiple sets as: $\bigcup_{i=1}^n S_i = S_1 \cup S_2 \cup ... \cup S_n$ Since the [union](Union%20of%20sets.md) of multiple sets necessarily includes all elements in all of these sets, the union is associative, meaning that $(S_1 \cup S_2)\cup S_3= S_1 \cup (S_2\cup S_3)= S_1 \cup S_2\cup S_3$ #MathematicalFoundations/SetTheory