For other uses see Sequence (disambiguation).
In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and the exact same elements can appear multiple times at different positions in the sequence.
For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers (2, 4, 6,...).
What are notions of sequences in mathematics, some of which (e.g., exact sequence) are not covered by the notations introduced below.
A sequence may be denoted (a1, a2, ...). For shortness, the notation (an) is also used.
A more formal definition of a finite sequence with terms in a set S is a function from