"the cake") and a group of players. A division is a partition of into disjoint subsets: , one subset per player.

The set can be of various types:
* may be a finite set of indivisible items, for example: , such that each item should be given entirely to a single person.
* may be an infinite set representing a divisible resource, for example: money, or a cake. Mathematically, a divisible resource is often modeled as a subset of a real space, for example, the section [0,1] may represent a long narrow cake, that has to be