Talk:Cardinality of Infinite Sigma-Algebra is at Least Cardinality of Continuum

Disjoint family of sets
How does the statement

"Thus the sets in $\family {F_i}$ are disjoint."

follow from the lines above? The reasoning seems to be that for an arbitrary $\ds S \in \cup_{k \mathop \in \N} F_k$, there is some first $k$ such that $S \in F_k$. And thus, the sets are disjoint? It might follow, but I don't! ––St.nerol (talk) 20:34, 4 September 2023 (UTC)
 * It is wrong because $F_2=X$, isn't it? --Usagiop (talk) 21:14, 4 September 2023 (UTC)
 * Oh, I didn't even think of that! I was more confused about the reasoning itself. Even if there is some first set in a sequence containing a given element, it says nothing about its containment in later sets. –St.nerol (talk) 10:55, 5 September 2023 (UTC)