ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4269 on D77: Set union
Countable set union with empty set
Formulation 0
Let $\emptyset$ be the D13: Empty set.
Let $X_n$ be a D11: Set for each $n \in \mathbb{N}$ such that
(i) \begin{equation} X_0 = \emptyset \end{equation}
Then \begin{equation} \bigcup_{n \in \mathbb{N}} X_n = \bigcup_{n \in \mathbb{N} + 1} X_n \end{equation}