A cartesian product may be constructed from a finite number of factors, each of which may be a set or algebraic structure. The term tuple will refer to an element of a cartesian product.
Note that the rules for tuples are quite different to those for sequences. Sequences are elements of a cartesian product of n copies of a fixed set (or algebraic structure) while tuples are elements of cartesian products where the factors may be different sets (structures). The semantics for tuples are quite different to those for sequences. In particular, the parent cartesian product of a tuple is fixed once and for all. This is in contrast to a sequence, which may grow and shrink during its life (thus implying a varying parent cartesian product).