Affine space/K/Polynomial/Vanishing set/Definition

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}F\in K[X_{1},\ldots ,X_{n}]}$ denote a polynomial in ${\displaystyle {}n}$ Variables. The set

${\displaystyle {\left\{P\in K^{n}\mid F(P)=0\right\}}}$

is called the vanishing set (or zero set) of ${\displaystyle {}F}$.