\begin{definition}[Definition:Geometric Tangent Vector]
Let $\R^n_a$ be a geometric tangent space.
A '''geometric tangent vector to $\R^n$ at $a \in \R^n$''' is an element $v \in \R^n_a$.
It can be denoted by $\tuple {a, v}$, $v_a$ or $\valueat v a$.
\end{definition}