Affine space (reviewed)

Affine space $\mathbb{A}^n(K)$ of dimension $n$ over a field $K$ is the set $K^n$.

If $P=(x_1,\dots,x_n)$ is a point in $\mathbb{A}^n(K)$, the $x_i$ are called the affine coordinates of $P$. Thus $$ \mathbb{A}^n(K) = \{(x_1,\dots,x_n)\mid x_1,\dots,x_n\in K\}. $$