The restriction of [[Union (setsset theory)|unions]] to disjoint unions is an important one; however, in the formal specification of symbolic combinatorics, it is too much trouble to keep track of which sets are disjoint. Instead, we make use of a construction that guarantees there is no intersection (''be careful, however; this affects the semantics of the operation as well''). In defining the ''combinatorial sum'' of two sets <math>\mathcal{A}</math> and <math>\mathcal{B}</math>, we mark members of each set with a distinct marker, for example <math>\circ</math> for members of <math>\mathcal{A}</math> and <math>\bullet</math> for members of <math>\mathcal{B}</math>. The combinatorial sum is then:
