Let $k$ be a field, let $n\in \mathbb N$, and let $R=k[x_1,\dots,x_n]$. For every ideal $\mathfrak a\trianglelefteq R$ and every subset $X\subset \mathbb A_k^n$, one has
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\begin{align*}
\mathfrak a \subset I(V(\mathfrak a)).
\end{align*}