Bell Number/Examples

Examples of Bell Numbers

Example: $B_2$

From the definition of Bell number, $B_2$ is the number of ways a set with $2$ elements can be partitioned.

$\set {a, b}$

$\set {\set a, \set b}$

$B_2 = 2$

Example: $B_3$

From the definition of Bell number, $B_3$ is the number of ways a set with $3$ elements can be partitioned.

$\set {a, b, c}$

$\set {\set a, \set {b, c} }$

$\set {\set b, \set {a, c} }$

$\set {\set c, \set {a, b} }$

$\set {\set a, \set b, \set c}$

$B_3 = 5$