Total Number of Set Partitions/Examples/4

Example of Cardinality of Set Partitions
Let $S$ be a set whose cardinality is $4$.

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

Thus: