Let \((X, \mathscr{A})\) be a measurable space. Show that there cannot be a \(\sigma\)-algebra \(\mathscr{A}\) which contains countably infinitely many sets.

[recall that \(A \in \mathscr{A}\) is an atom if \(A\) contains no proper subset \(\emptyset eq B \in \mathscr{A}\). Show that \(\# \mathscr{A}=\# \mathbb{N}\) implies that \(\mathscr{A}\) has countably infinitely many atoms. This will lead to a contradiction.]