  The big-line-big-clique conjecture states that for all $k,\ell\geq2$ there is
an integer $n$ such that every finite set of at least $n$ points in the plane
contains $\ell$ collinear points or $k$ pairwise visible points. We show that
this conjecture is false for infinite point sets, by constructing a countably
infinite point set with no 4 collinear points and no 3 pairwise visible points.
