Affine space/Affine basis/Definition

A family of points ${\displaystyle {}P_{i}\in E}$, ${\displaystyle {}i\in I}$, in an affine space ${\displaystyle {}E}$ over a ${\displaystyle {}K}$-vector space ${\displaystyle {}V}$ is called an affine basis of ${\displaystyle {}E}$, if there exists an ${\displaystyle {}i_{0}\in I}$ such that the family of vectors

${\displaystyle {\overrightarrow {P_{i_{0}}P_{i}}},i\in I\setminus \{i_{0}\},}$

is a basis of ${\displaystyle {}V}$.