Lets say we have a set $S$ of $N$ ($N\geq 3$) finite nonempty sequences of numbers, each of different length. Is the relation of "having some number or numbers in common" transitive on $S$? I have no idea how to even start proving or disproving this statement.
2026-03-28 18:12:47.1774721567
Common numbers in sequences
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That relation is definitely not transitive. Think about $$ A = \{1,2,3\}, B = \{3,4,5,6\}, \textrm{ and } C = \{6,7,8,9,10\}.$$
Then $ArB$ and $BrC$, but $A$ is not related to $C$.