What is the difference between Partition and Division?
I will explain this with an example :
Consider a set $S$ which contains a collections of sets with a constant k such that:
$$ S = \{ \{S_1\}, \{S_2\}, \{S_3\},\{S_4\},..........\{S_k\} \}$$
In Partition of Set S :
Then we can form the set again by
$ S=S_1\cup S_2\cup S_3\cup S_4...........\cup S_k$
$where\ S_i\cap S_j = \phi$
$and\ i\neq j\ and\ i,j\in \mathcal{N} $
In Division of Set S :
We just have this
$ S=S_1\cup S_2\cup S_3\cup S_4...........\cup S_k$