Consider the metric space $\bf R$ with the standard Euclidean metric $d$ and let $F(\bf R)$ denote the collection of all finite subsets of $\bf R$. Endow $F(\bf R)$ with the Hausdorff metric $d_H$. See Wikipedia for the definition of $d_H$.
Is $F(\bf R)$ complete w.r.t. $d_H$?