Definition:Set Partition/Definition 2

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Definition

Let $S$ be a set.


A partition of $S$ is a set of non-empty subsets $\Bbb S$ of $S$ such that each element of $S$ lies in exactly one element of $\Bbb S$.


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 demonstration that all elements of such a partition are indeed non-empty.


Also see


Sources