[bmacho]

> 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.