Definition:Disjoint Union (Set Theory)/2 Sets

Definition
Let $I$ be a doubleton, say $I := \set {0, 1}$.

Let $\family {S_i}_{i \mathop \in I}$ be an $I$-indexed family of sets.

Then the disjoint union of $\family {S_i}_{i \mathop \in I}$ is defined as the set: