Euclidean space is an affine space

Question

I know the fact that each Euclidean space is an affine space.But I was troubled by the definition of affine space. see Vector Spaces versus Affine Spaces

The definition of an affine space consists a triple $(A,V,\phi)$.Take the Euclidean space $\Bbb R^2$ for example,what is the set $A$ and what is the vector space $V$?

Answer 1

For a linear space $V$, the corresponding affine space is $(V, V, \phi)$ where $\phi(v, w) =w-v$ (or $v+w$, depending on your definition) is the canonical action.