Total Number of Set Partitions/Examples/3

Example of Total Number of Set Partitions
Let $S$ be a set whose cardinality is $3$.

Then the number of partitions of $S$ is $5$.

Proof
Let $p \paren n$ denote the cardinality of the set of partitions of a set whose cardinality is $n$.

From Total Number of Set Partitions, $p \paren n$ is the $n$th Bell number $B_n$.

Thus: