If $n$ is a positive integer, then an ordered $n$-tuple is a sequence of $n$ real numbers $\left(v_{1}, v_{2}, \ldots, v_{n}\right) .$ The set of all ordered $n$-tuples is called $\boldsymbol{n}$-space and is denoted by $R^{n}$. You can think of the numbers in an $n$-tuple $\left(v_{1}, v_{2}, \ldots, v_{n}\right)$ as either the coordinates of a generalized point or the components of a generalized vector, depending on the geometric image you want to bring to mind - the choice makes no difference mathematically, since it is the algebraic properties of $n$-tuples that are of concern.