\begin{definition}[Definition:Sequence/Infinite Sequence]
An '''infinite sequence''' is a sequence whose domain is infinite.
That is, an '''infinite sequence''' is a sequence that has infinitely many terms.
Hence for an '''infinite sequence''' $\sequence {s_n}_{n \mathop \in \N}$ whose range is $S$, $\sequence {s_n}_{n \mathop \in \N}$ is an element of the set of mappings $S^{\N}$ from $\N$ to $S$.
On {{ProofWiki}} all sequences are '''infinite sequence''' unless explicitly specified otherwise.
\end{definition}