ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4268 on D77: Set union
Finite set union with empty set
Formulation 0
Let $\emptyset$ be the D13: Empty set.
Let $X_1, \ldots, X_{N + 1}$ each be a D11: Set such that
(i) \begin{equation} X_{N + 1} = \emptyset \end{equation}
Then \begin{equation} \bigcup_{n = 1}^{N + 1} X_n = \bigcup_{n = 1}^N X_n \end{equation}