Chapter 12: partition

$$\begin{align*} & \left\{ A_{i}\right\} _{i\in I}=\left\{ A_{i}\middle|i\in I\right\} \text{ is a partition of a set }A\\ \Leftrightarrow & \begin{cases} \forall i\in I\left(A_{i}\ne\emptyset\right)\\ A=\bigcup\limits _{i\in I}A_{i}\\ \forall i,j\in I\left(i\ne j\Rightarrow A_{i}\cap A_{j}=\emptyset\right) \end{cases} \end{align*}$$

https://proofwiki.org/wiki/Definition:Set_Partition