A union where duplicate elements from two sets are separately included (which is not the case with standard union). For example, given two sets A₁, A₂ their disjoint union, denoted A₁⊔A₂, may be identified with (A₁×{1})∪(A₂×{2}). If x is common to both A₁ and A₂, its first version appears as (x,1) in A₁⊔A₂ and the second copy as (x,2).