For a metric space ▫$X$▫, let ▫$\mathsf FX$▫ be the space of all nonempty finite subsets of ▫$X$▫ endowed with the largest metric ▫$d^1_{\mathsf FX}$▫ such that for every ▫$n\in\mathbb N$▫ 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 ▫$\mathsf F^1\!X=(\mathsf FX,d^1_{\mathsf FX})$▫ and prove that it coincides with the space ▫$\mathsf Z^1\!X$▫ of nonempty compact subsets of ▫$X$▫ that have zero length (defined with the help of graphs). We prove that each subset of zero length in a metric space has 1-dimensional Hausdorff measure zero. A subset ▫$A$▫ of the real line has zero length if and only if its closure is compact and has Lebesgue measure zero. 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 to have zero length
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