Definition:Real Sequence/Notation

Notation for Real Sequence
The notation for a real sequence is conventionally of the form $\sequence {a_n}$, where it is understood that:
 * the domain of $\sequence {a_n}$ is the natural numbers: either $\set {0, 1, 2, 3, \ldots}$ or $\set {1, 2, 3, \ldots}$
 * the range of $\sequence {a_n}$ is the set of real numbers $\R$.

However, some sources use the notation of mappings to explicitly interpret a real sequence as a real-valued function:
 * $f: \N \to \R$

Hence the $n$th term can be seen denoted in two ways:
 * $\sequence {a_n}$
 * $\map f n$