\$$\mathbb{R ^ n} = \mathbb{R} \times \mathbb{R} \times \ldots \mathbb{R}\$$ is the set of all n-tuples of real numbers. This is n-dimensional Cartesian space.

The members of \$$\mathbb{R^n}\$$ are called _vectors_, and \$$\mathbb{R^n}\$$ is a _vector space_.

To be more specific, we can refer to the members of \$$R^n\$$ as n-vectors.

An n-vector, then, is simply an n-tuple, a list, of n real numbers.