of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set.

For example, (M, A, R, Y) is a sequence of letters with the letter "M" first and "Y" last. This sequence differs from (A, R, M, Y). Also, the sequence , which contains the number at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of positive even integers