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For a metric space $X$, let $\mathsf FX$ be the space of all nonempty finitesubsets of $X$ endowed with the largest metric $d^1_{\mathsf FX}$ such that forevery $n\in\mathbb N$ the map $X^n\to\mathsf FX$, $(x_1,\dots,x_n)\mapsto\{x_1,\dots,x_n\}$, is non-expanding with respect to the $\ell^1$-metric on$X^n$.  We study the completion of the metric space $\mathsf F^1\!X=(\mathsfFX,d^1_{\mathsf FX})$ and prove that it coincides with the space $\mathsfZ^1\!X$ of nonempty compact subsets of $X$ that have zero length (defined withthe help of graphs). We prove that each subset of zero length in a metric spacehas 1-dimensional Hausdorff measure zero. A subset $A$ of the real line haszero length if and only if its closure is compact and has Lebesgue measurezero. On the other hand, for every $n\ge 2$ the Euclidean space $\mathbb R^n$contains a compact subset of 1-dimensional Hausdorff measure zero that fails tohave zero length.

The completion of the hyperspace of finite subsets, endowed with the $\ell^1$-metric