We say that a function
$h\,:\,\mathbb{R}\,\to \,\mathbb{R}$
is a Hamel function
$(h\,\in \,\text{HF)}$
if
$h$
, considered as a subset of
${{\mathbb{R}}^{2}},$
is a Hamel basis for
${{\mathbb{R}}^{2}}.$
We show that
$\text{A}\left( \text{HF} \right)\,\ge \,\omega$
, i.e., for every finite
$F\,\subseteq \,{{\mathbb{R}}^{\mathbb{R}}}$
there exists
$f\,\in \,{{\mathbb{R}}^{\mathbb{R}}}$
such that
$f\,+\,F\,\subseteq \,\text{HF}$
. From the previous work of the author it then follows that
$\text{A}\left( \text{HF} \right)\,=\,\omega$
.