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:1, 1 , 2 , 5 , 15 , 52 , 203, 877, 4140, 21147, 115975 (See also Breakdown By Number Of Subsets/equivalence Classes .) PARTITIONS OF A SET In general, ''B''''n'' is the number of Partitions of a set of size ''n''. A partition of a set ''S'' is defined as a set of nonempty, pairwise disjoint subsets of ''S'' whose union is ''S''. For example, ''B''3 = 5 because the 3-element set {''a'', ''b'', ''c''} can be partitioned in 5 distinct ways: : : : :
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