= Hamming distance between unlabelled bipartitions
{c}
{title2=$\Delta(S,T)=\min\{|S\triangle T|,|S\triangle T^c|\}$}
This <Hamming distance> on partitions identifies a group with its complement because exchanging the two group names does not change the partition. Complementation is an <isometry> of the ordinary <Hamming distance>, so minimizing over this two-element group action gives a quotient metric and preserves the <triangle inequality>. Negating a zero-one indicator is not complementation; with $\pm1$ membership vectors, it is.
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