## Sequence |

in

, amathematics **sequence**is an enumerated collection of objects in which repetitions are allowed and does matter. like aorder , it containsset (also calledmembers *elements*, or*terms*). the number of elements (possibly infinite) is called the*length*of the sequence. unlike a set, the same elements can appear multiple times at different positions in a sequence, and order does matter. formally, a sequence can be defined as a whose domain is either the set of thefunction (for infinite sequences) or the set of the firstnatural numbers *n*natural numbers (for a sequence of finite length*n*).the position of an element in a sequence is its

*rank*or*index*; it is the natural number for which the element is the image. the first element has index 0 or 1, depending on the context or a specific convention. when a symbol is used to denote a sequence, the*n*th element of the sequence is denoted by this symbol with*n*as subscript; for example, the*n*th element of thefibonacci sequence *f*is generally denoted*f*_{n}.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 (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. sequences can be

, as in these examples, orfinite , such as the sequence of allinfinite even (2, 4, 6, ...). inpositive integers andcomputing , finite sequences are sometimes calledcomputer science ,strings orwords , the different names commonly corresponding to different ways to represent them inlists ; infinite sequences are calledcomputer memory . the empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.streams - examples and notation
- formal definition and basic properties
- limits and convergence
- series
- use in other fields of mathematics
- see also
- notes
- references
- external links

In **sequence** is an enumerated collection of objects in which repetitions are allowed and *elements*, or *terms*). The number of elements (possibly infinite) is called the *length* of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and order does matter. Formally, a sequence can be defined as a *n* natural numbers (for a sequence of finite length *n*).

The position of an element in a sequence is its *rank* or *index*; it is the natural number for which the element is the image. The first element has index 0 or 1, depending on the context or a specific convention. When a symbol is used to denote a sequence, the *n*th element of the sequence is denoted by this symbol with *n* as subscript; for example, the *n*th element of the *F* is generally denoted *F*_{n}.

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 (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be * finite*, as in these examples, or