Let \(\mathcal A=(A,V_A,v)\) be an \(n\)-dimensional affine space for a natural number \(n\ge 0\). Let \(U\subseteq \mathcal A\) be an affine subspace. * If \(\operatorname{dim}(U)=-1\), then \(U=\emptyset\). * If \(\operatorname{dim}(U)=0\), then \(U\) is called a point. * If \(\operatorname{dim}(U)=1\), then \(U\) is called a line. * If \(\operatorname{dim}(U)=2\), then \(U\) is called a plane. * If \(\operatorname{dim}(U)=s\) with \(s < n\), then \(U\) is called an \(s\)-dimensional hyperplane.
