Definition:Trivial Partition
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Definition
Let $S$ be a set such that $S \ne \O$.
There are two partitions on $S$ which are referred to as the trivial partitions on $S$:
Singleton Partition
The singleton partition on $S$ is defined as:
- $\PP = \set S$
That is, it is a partition with only one component.
Partition of Singletons
The partition of singletons on $S$ is defined as:
- $\PP = \set {\set x: x \in S}$
That is, it is a partition such that every component is a singleton.