EDB — 036

Exercises

1. [036] Let \(I\) be a family of indices and \(B_ i,A_ i\) sets, for \(i∈ I\), such that \(| A_ i|≤ | B_ i|\); suppose that the sets \(B_ i\) are pairwise disjoint. Show that

   \[ \left|⋃_{i∈ I} A_ i\right| ≤ \left|⋃_{i∈ I} B_ i\right|~ . \]

   (In your opinion, is it possible to prove this result without using the axiom of choice, at least in the case in which \(I\) is countable?)

   Solution 1

   [037]↺↻