- #61

member 587159

This problem is of the devil mhh, the following is a cheapshot

Take a sequence of pairwise disjoint nonempty subsets [itex]S_n\in\Sigma, n\in\mathbb N[/itex]. Then

[tex]

\mathcal P(\mathbb N) \setminus \{\emptyset, \mathbb N\} \to \Sigma, \quad A \mapsto \bigcup _{x\in A} S_x

[/tex]

is injective, because of disjointedness.

Now we are going somewhere. Or course, the question is why such a sequence exists. How can we construct one?