I am reading "A First Course In Probability" by Sheldon Ross, and I am having difficulty solving one of the problems in the book:
For any sequence of events $E_1$, $E_2$, $\ldots\,$, define a new sequence $F_1$, $F_2$, $\ldots\,$ such that all the $F_i$ are disjoint and the union from $i=1$ to $n$ of $E_i$ is equal to the union from $i=1$ to $n$ of $F_i$ for any natural number $n$.