Let $B$ be a block of a set $X$ under the operation of a group $G$. Let $GB=\bigcup_{g\in G}gB$. Then, is $(gB)_{g\in G}$ the associated partition of $X$, or is it $(Y)_{Y\in GB}$? This concerns the proof of disjointness. If the former is the partition, then I have to show $g\ne g'$ implies $gB\cap g'B=\emptyset$. If the latter is the partition, then I have to show that $gB\ne g'B$ implies $gB\cap g'B=\emptyset$. So, which is it?
2026-03-29 08:44:58.1774773898
Block system partitions set
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