Definition:Sequence

Informal Definition
A sequence is a set of objects which is listed in a specific order, one after another.

Thus one can identify the elements of a sequence as being the first, the second, the third, ... the $n$th, and so on.

Formal Definition
A sequence is a mapping whose domain is a subset of the set of natural numbers $\N$.

It can be seen that a sequence is an instance of a family of elements indexed by $\N$.

Also defined as
Some sources, generally expositions of set theory, define a sequence as a mapping whose domain is an ordinal.

In such cases, the natural numbers $\N$ are defined as the finite ordinals, meaning the two definitions are in complete agreement.

Note, however, that this definition of sequence extends to the transfinite ordinals.

Also see

 * Definition:Integer Sequence
 * Definition:Rational Sequence
 * Definition:Real Sequence
 * Definition:Complex Sequence


 * Definition:Arithmetic Function, which can be considered as an example of an infinite sequence