Let $E_0, E_1, E_2, \ldots$ each be a
D11: Set such that
| (i) |
\begin{equation}
E_0 \subseteq E_1 \subseteq E_2 \subseteq \cdots
\end{equation}
|
Let $F_0, F_1, F_2, \ldots$ each be a
D11: Set such that
| (i) |
\begin{equation}
F_0 : = E_0
\end{equation}
|
| (ii) |
\begin{equation}
\forall \, n \in 1, 2, 3, \ldots
: F_n : = E_{n + 1} \setminus E_n
\end{equation}
|
Then
| (1) |
\begin{equation}
\forall \, n, m \in \mathbb{N} \, (n \neq m \quad \Rightarrow \quad F_n \cap F_m = \emptyset)
\end{equation}
|
| (2) |
\begin{equation}
\bigcup_{n \in \mathbb{N}} E_n = \bigcup_{n \in \mathbb{N}} F_n
\end{equation}
|
