or sum, n. 1. the set of elements that belong to either of a given pair of sets, written S ∪ T, and often called cup; if the two circles in the figure represent S and T respectively, the shaded area represents their union.
2. the binary operation that forms such a set from two given sets. 3. more generally, over any collection, C, of subsets C_α of a given set X (indexed by α ∈ A), the set each of whose elements lies in at least one member of the collection. This is denoted
∪_α∈A C_α or ∪C;
in particular, ∪∅ = ∅. See also intersection.