The partition of sets is a very important subject, especially in probability theory, Lesbegue integral, among others. In the previous post we saw equivalence relations and they are directly related to the notion of partition of sets. Definition Definition (Partition) Let $A$ be a nonempty set ($A\neq \emptyset$) and a family $\mathcal{F}$ of nonempty subsets of $A$. The partition definition of $A$ is valid if the following statements are true: (a) any two elements of $\mathcal{F}$ are either equal or disjoint;