We say that a set S {\displaystyle S} has a finite partition into **subsets** S 1 , … , S n {\displaystyle S_{1},\dots ,S_{n}} , if S = S i ∪ ⋯ ∪ S n {\displaystyle S=S_{i}\cup \dots \cup S_{n}} , where the **subsets** are pairwise disjoint, that is, S i ∩ S j = ∅ {\displaystyle S_{i}\cap S_{j}=\emptyset } , if i ≠ j {\displaystyle i\neq j} . (We do not require that the **subsets** be nonempty.)

2007, Judith D. Sally, Paul J. Sally, Jr., Roots to Research: A Vertical Development of Mathematical Problems, American Mathematical Society, page 280