> Vectors are functions whose input space are discrete dimensions. This is _also_ true. But the fact that finite dimensional real vectors can be viewed as a sp

> Vectors are functions whose input space are discrete dimensions. This is _also_ true. But the fact that finite dimensional real vectors can be viewed as a special case of set-theoretic functions or as a special case of real functions on a discrete finite space is probably less useful than the opposite: the set of real functions have a vector-space structure, and you can use all the neat theorems about (finite or infinite dimensional) vector spaces. Well, at least the article is about the latter direction.