Definition:Range of Sequence

Definition

Let $\sequence {x_n}_{n \mathop \in A}$ be a sequence.

The range of $\sequence {x_n}$ is the set:

$\set {x_n: n \mathop \in A}$

Also known as

Some treatments of this subject refer to the range of a sequence as the associated set of the sequence.

Some treatments do not bother to give it a name at all, merely referring to it as the set of its elements.

In keeping with the naming convention on this site it would make sense to refer to this object as the image of (the sequence) $\sequence {x_n}$.

However, this is rarely seen in the published literature.