In mathematics, there is a class of problems, all of which study the spatial region formed by dividing space. For example, there are n straight lines on the plane. How many areas does it divide the plane into? A complete description of the problem and related results can be found in the entry "Spatial area". The division of a set is also called the division of a set.

Division in discrete mathematics

In discrete mathematics, partition means that the set P of the nonempty subset of nonempty set A satisfies the following two conditions: each element of 1 A belongs to a set in p; 2. If A 1 and A2 are different elements in P, then A 1 ∩ A2 = φ. Division is also called quotient set. A set in p is called a block or unit in a partition.

Because the members of the partition of set A are subsets of A, the partition is a subset of the power set P(A) of A, that is, the partition can be regarded as a special subset of P(A).