Content deleted Content added
Line 15:
===Set partitions===
{{main article|Partition of a set}}
[[File:Bell numbers subset partial order.svg|thumb|right|Partitions of sets can be arranged in a partial order, showing that each partition of a set of size ''n'' "uses" one of the partitions of a set of size
[[File:Set partitions 5; circles.svg|thumb|The 52 partitions of a set with 5 elements]]
In general, <math>B_n</math> is the number of [[partition of a set|partitions]] of a set of size <math>n</math>. A partition of a set <math>S</math> is defined as a family of nonempty, pairwise disjoint subsets of <math>S</math> whose union is <math>S</math>. For example, <math>B_3 = 5</math> because the 3-element set <math>\{a,b,c\}</math> can be partitioned in 5 distinct ways:
| |||