\begin{definition}[Definition:Dimension of Vector Space/Vector]
Informally, an element of an $n$-dimensional vector space is often referred to as an '''$n$-dimensional vector'''. 
It must be understood that this is no more than a convenient shorthand. It is not the ''vector'' which possesses the dimensionality, but the ''space in which it is embedded''.
Category:Definitions/Vectors
Category:Definitions/Dimension of Vector Space
\end{definition}