= Countability of pairwise disjoint open disks
{title2=$|\mathcal D|\le\aleph_0$}
Every family of pairwise disjoint nonempty open disks in the plane is countable. The <density of the rational numbers> gives each disk a point of the <countable set> $\mathbb Q^2$. Fixing an enumeration and taking the first point in each disk yields an <injection> from disks to labels. This argument requires no countable choice of representatives and is useful when geometric separation would otherwise produce an uncountable family.
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