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Bondy's theorem : ウィキペディア英語版 | Bondy's theorem In mathematics, Bondy's theorem is a bound on the number of elements needed to distinguish the sets in a family of sets from each other. It belongs to the field of combinatorics, and is named after John Adrian Bondy, who published it in 1972.〔.〕 ==Statement== The theorem is as follows: :Let ''X'' be a set with ''n'' elements and let ''A''1, ''A''2, ..., ''A''''n'' be distinct subsets of ''X''. Then there exists a subset ''S'' of ''X'' with ''n'' − 1 elements such that the sets ''A''''i'' ∩ ''S'' are all distinct. In other words, if we have a 0-1 matrix with ''n'' rows and ''n'' columns such that each row is distinct, we can remove one column such that the rows of the resulting ''n'' × (''n'' − 1) matrix are distinct.〔, Section 12.1.〕〔, Section 4.1.〕
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