Exercises
[020] Prerequisites:[024].(Solved on 2022-10-25) Given \(A\) non-empty set show that there is a bijection \(f:A→ B\) between \(A\) and a set \(B\) disjoint from \(A\).
More generally, let \(I\) a non-empty set of indexes, and \(A_ i\) a family of non-empty sets indexed by \(i∈ I\); 1 show that there are bijections \(f_ i:A_ i→ B_ i\), where the sets \(B_ i\) enjoy \(∀ i∈ I,∀ j∈ I, B_ i∩ A_ j=∅\) and for \(j≠ j\) also \( B_ i∩ B_ j=∅\).
Solution 1