Let $k$ be a field, let $n \in \mathbb{N}$, and let $X \subset \mathbb{A}^n_k$ be an [affine variety](/page/Affine%20Variety). Then there exist $m \in \mathbb{N}$ and polynomials $f_1, \ldots, f_m \in k[x_1, \ldots, x_n]$ such that
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\begin{align*}
X = V(f_1, \ldots, f_m).
\end{align*}