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C×D denotes the Cartesian product of two sets C and D. It is defined as the set of all ordered pairs (c, d) where c is an element of C and d is an element of D. In symbols: C×D = { (c, d) | c ∈ C and d ∈ D }.

The Cartesian product is a subset of the product of the ambient universes from which C and D are drawn. Its size, when both sets are finite, is the product of their cardinalities: |C×D| = |C|·|D|. If either C or D is empty, then C×D is empty. The elements of C×D are pairs, and there are natural projection maps to C and to D that extract the first and second components, respectively.

Common examples illustrate the concept. If C = {1, 2} and D = {a, b}, then C×D = { (1, a), (1, b), (2, a), (2, b) }. If C and D are subsets of a common universe, C×D is a subset of that universe’s product with itself, containing all possible pairings of elements from C with elements from D.

C×D has important roles in mathematics. A relation from C to D is any subset of C×D, and a function from C to D is a special relation that assigns exactly one element of D to each element of C. In topology, if C and D are topological spaces, the product topology on C×D is a standard construction.

Note that the symbol × is also used for other binary operations, such as the cross product of vectors in three-dimensional space. Context determines whether C×D refers to a Cartesian product of sets or another operation.