Definition:Set Partition

Definition
Let $S$ be a set.

Also known as
A partition is sometimes called a decomposition.

This same definition is also encountered in the field of combinatorics.

Also defined as
Some sources do not impose the condition that all sets in $\Bbb S$ are non-empty.

This is most probably more likely to be an accidental omission rather than a deliberate attempt to allow $\O$ to be an element of a partition.

The point is minor; proofs of partitionhood usually include a demostration that all elements of such a partition are indeed non-empty.

Also see

 * Equivalence of Definitions of Set Partition


 * Definition:Partition (Topology): a slightly more specialized definition.