\begin{definition}[Definition:Affine Algebraic Set]
Let $K$ be a field.
Let $A = K \sqbrk {X_1, \ldots, X_n}$ be the ring of polynomial functions in $n$ variables over $K$.
Then a subset $X \subseteq K^n$ is an '''affine algebraic set''' {{iff}} it is the zero locus of some set $T \subseteq A$.
\end{definition}