Sequence
![An infinite sequence of real numbers (in blue). This sequence is neither increasing, nor decreasing, nor convergent, nor Cauchy. It is, however, bounded.](/Images/godic/202501/30/Cauchy_sequence_illustration2.svg5215.png")
![A tiling with squares whose sides are successive Fibonacci numbers in length.](/Images/godic/202501/30/Fibonacci_blocks.svg5215.png")
![The plot of a convergent sequence (an) is shown in blue. From the graph we can see that the sequence is converging to the limit zero as n increases.](/Images/godic/202501/30/Converging_Sequence_example.svg5215.png")
![The plot of a Cauchy sequence (Xn), shown in blue, as Xn versus n. In the graph the sequence appears to be converging to a limit as the distance between consecutive terms in the sequence gets smaller as n increases. In the real numbers every Cauchy sequence converges to some limit.](/Images/godic/202501/30/Cauchy_sequence_illustration.svg5216.png")
In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is a convex subset of the set of integers, such as ![\{0, 1, 2, ...\}](/Images/godic/202501/30/35f44b554996fc2e94cf37eed05faae75216.png")
, ![\{1, 2, ...\}](/Images/godic/202501/30/dc6df79fde491a68b8fae60ad07d01345216.png")
, ![\{0, 1, 2, ..., n\}](/Images/godic/202501/30/5ac6a994532510cb5ff9f81b0b0205f65216.png")
, or ![\{..., -1, 0, 1, 2, ...\}](/Images/godic/202501/30/abe84e639e6134511280c73efb16423e5216.png")
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