A partition of a set is a family of pairwise disjoint nonempty subsets whose union is . Every equivalence relation defines a partition into equivalence classes, and conversely belonging to the same cell of a partition defines an equivalence relation. The nonempty colour classes of a finite colouring form a finite partition.
A colouring assigns to each member of a set a colour in another set . Its nonempty fibres form a partition of a set. The colour set may be infinite; a finite colouring is the special case with finitely many colours. A homogeneous set for a colouring of finite subsets has all its subsets of the specified size assigned one colour.
