Definition:Sequence/Infinite Sequence

Definition
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 all sequences are infinite sequence unless explicitly specified otherwise.

Also known as
Treatments of this subject which approach the definition of a sequence from the direction of ordered tuples offer the term $\omega$-tuple for the concept of a tuple whose domain is (countably) infinite.

Some sources use the term denumerable sequence.