If n is a natural number and A is an arbitrary set, the expression An is often used to denote the set of ordered n-tuples of elements of A. This is equivalent to letting An denote the set of functions from the set {0, 1, 2, ..., n???1} to the set A; the n-tuple (a0, a1, a2, ..., an???1) represents the function that sends i to ai.