  In this paper we are interested in finding and evaluating cardinal
characteristics of the continuum that appear in large-scale topology, usually
as the smallest weights of coarse structures that belong to certain classes
(indiscrete, inseparated, large) of finitary or locally finite coarse
structures on $\omega$. Besides well-known cardinals $\mathfrak b,\mathfrak
d,\mathfrak c$ we shall encounter two new cardinals $\mathsf \Delta$ and
$\mathsf \Sigma$, defined as the smallest weight of a finitary coarse structure
on $\omega$ which contains no discrete subspaces and no asymptotically
separated sets, respectively. We prove that $\max\{\mathfrak b,\mathfrak
s,\mathrm{cov}(\mathcal N)\}\le\mathsf \Delta\le\mathsf
\Sigma\le\mathrm{non}(\mathcal M)$, but we do not know if the cardinals
$\mathsf \Delta,\mathsf \Sigma,\mathrm{non}(\mathcal M)$ can be separated in
suitable models of ZFC.
