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:

$\sequence {a_n}$

$\map f n$