- E272
[038] Let \(C\) be a set, \(I\) a family of indexes, and then \(B_ i\) sets, for \(i\in I\); suppose the sets \(B_ i\) are pairwise disjoint; define \({\mathcal B}=\bigcup _{i\in I} B_ i\) for convenience; then show that
\begin{eqnarray} \forall i, |B_ i|\le |C|& \Rightarrow & \left|{\mathcal B}\right| \le \left|I\times C\right| \label{eqn:B_ i_ cup_ le_ times_ C}\\ \forall i, |B_ i|\ge |C|& \Rightarrow & \left|{\mathcal B}\right| \ge \left|I\times C\right|~ ~ . \end{eqnarray}Solution 1[[03B]]
EDB — 038
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Authors:
"Mennucci , Andrea C. G."
.
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