Let $k$ be a field and let $n\in \mathbb N$. For every ideal $I\trianglelefteq k[x_1,\dots,x_n]$, there exist an integer $r\in \mathbb N$ and polynomials $f_1,\dots,f_r\in k[x_1,\dots,x_n]$ such that
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\begin{align*}
V(I)=V(f_1,\dots,f_r)
\end{align*}
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as subsets of $\mathbb A_k^n$, where
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\begin{align*}
V(I)=\{a\in \mathbb A_k^n: f(a)=0 \text{ for every } f\in I\}
\end{align*}
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and
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\begin{align*}
V(f_1,\dots,f_r)=\{a\in \mathbb A_k^n: f_i(a)=0 \text{ for every } i\in\{1,\dots,r\}\}.
\end{align*}