> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/200-set-theory/topics/bell-number.md).

# Bell Number

**A Bell number** indicates the number of ways to *partition a set*.

It is denoted by Bn where n is the cardinality of the set.

Example:

Let S={1,2,3}, n = |S| = 3

The partitions are

1. ∅,{1,2,3}
2. {1},{2,3}
3. {1,2},{3}
4. {1,3},{2}
5. {1},{2},{3}

hence, B3 = 5