  Extending the classical result that the roots of a polynomial with
coefficients in $\mathbf{C}$ are continuous functions of the coefficients of
the polynomial, nonstandard analysis is used to prove that if $\mathcal{F} =
\{f_{\lambda} :\lambda \in \Lambda\}$ is a set of polynomials in
$\mathbf{C}[t_1,\ldots, t_n]$ and if $^*\mathcal{G} = \{g_{\lambda} :\lambda
\in \Lambda\}$ is a set of polynomials in $^*\mathbf{C}_0[t_1,\ldots, t_n]$
such that $g_{\lambda}$ is an infinitesimal deformation of $f_{\lambda}$ for
all $\lambda \in \Lambda$, then the nonstandard affine variety
$^*V_0(\mathcal{G})$ is an infinitesimal deformation of the affine variety
$V(\mathcal{F})$.
